Inifintely many solutions to Diophantine Equations of the form, 3 3 3 A X + B Y + B Z = CONSTANT, for A and B At Most, 100 By Shalosh B. Ekhad ------------------------------------------ Theorem Number , 1, : Let a(i), b(i), c(i) be defined in terms of the followi\ ng generating functions infinity ----- 2 \ i 293155 t + 888826 t - 29 ) a(i) t = --------------------------- / 2 ----- (t - 1) (t - 103682 t + 1) i = 0 infinity ----- 2 \ i 237169 t + 550798 t + 1 ) b(i) t = - --------------------------- / 2 ----- (t - 1) (t - 103682 t + 1) i = 0 infinity ----- 2 \ i 90601 t - 878594 t + 25 ) c(i) t = --------------------------- / 2 ----- (t - 1) (t - 103682 t + 1) i = 0 In Maple notation, these generating functions are (293155*t^2+888826*t-29)/(t-1)/(t^2-103682*t+1) -(237169*t^2+550798*t+1)/(t-1)/(t^2-103682*t+1) (90601*t^2-878594*t+25)/(t-1)/(t^2-103682*t+1) Then for all i>=0 we have 3 3 3 a(i) + 2 b(i) + 2 c(i) = -6859 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 2, : Let a(i), b(i), c(i) be defined in terms of the followi\ ng generating functions infinity ----- \ i ) a(i) t = 6 ( / ----- i = 0 2 127685126617965525465145750047142725430383115065843465863813509134811 t + 193427167735940568464986576348742012101549577438180983080641013313066 t / 2 - 5) / ((t - 1) (t / - 127779094158564803725247385052117994077978144119011378936223722704898 t + 1)) infinity ----- \ i ) b(i) t = - 4 ( / ----- i = 0 2 138471326149258413182220777576993559640716564656132104537883898361041 t + 109140286737799506877893126919568676261119240104803273584572506468142 t / 2 + 1) / ((t - 1) (t / - 127779094158564803725247385052117994077978144119011378936223722704898 t + 1)) infinity ----- \ i ) c(i) t = ( / ----- i = 0 2 271633972073109859595403031256395582348335162163190230452579415356697 t - 1262080423621341539835858649242644525955678381206931742942405034673458 t / 2 + 25) / ((t - 1) (t / - 127779094158564803725247385052117994077978144119011378936223722704898 t + 1)) In Maple notation, these generating functions are 6*(127685126617965525465145750047142725430383115065843465863813509134811*t^2+ 193427167735940568464986576348742012101549577438180983080641013313066*t-5)/(t-1 )/(t^2-127779094158564803725247385052117994077978144119011378936223722704898*t+ 1) -4*(138471326149258413182220777576993559640716564656132104537883898361041*t^2+ 109140286737799506877893126919568676261119240104803273584572506468142*t+1)/(t-1 )/(t^2-127779094158564803725247385052117994077978144119011378936223722704898*t+ 1) (271633972073109859595403031256395582348335162163190230452579415356697*t^2-\ 1262080423621341539835858649242644525955678381206931742942405034673458*t+25)/(t -1)/(t^2-127779094158564803725247385052117994077978144119011378936223722704898* t+1) Then for all i>=0 we have 3 3 3 a(i) + 3 b(i) + 3 c(i) = -19683 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 3, : Let a(i), b(i), c(i) be defined in terms of the followi\ ng generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 2635464015703912671535499399 t + 56970495786013982167267438034 t - 25 ---------------------------------------------------------------------- 2 (t - 1) (t - 37931065328365933079238232898 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 2 (919542334937461195184104613 t + 9917904901738519684598247638 t + 5) - ----------------------------------------------------------------------- 2 (t - 1) (t - 37931065328365933079238232898 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 1180218665948944222484334377 t - 22855113139300905982049038906 t + 17 ---------------------------------------------------------------------- 2 (t - 1) (t - 37931065328365933079238232898 t + 1) In Maple notation, these generating functions are (2635464015703912671535499399*t^2+56970495786013982167267438034*t-25)/(t-1)/(t^ 2-37931065328365933079238232898*t+1) -2*(919542334937461195184104613*t^2+9917904901738519684598247638*t+5)/(t-1)/(t^ 2-37931065328365933079238232898*t+1) (1180218665948944222484334377*t^2-22855113139300905982049038906*t+17)/(t-1)/(t^ 2-37931065328365933079238232898*t+1) Then for all i>=0 we have 3 3 3 a(i) + 4 b(i) + 4 c(i) = -27 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 4, : Let a(i), b(i), c(i) be defined in terms of the followi\ ng generating functions infinity ----- 2 \ i 300611646373 t + 1053397696054 t - 27 ) a(i) t = -------------------------------------- / 2 ----- (t - 1) (t - 208211515202 t + 1) i = 0 infinity ----- 2 \ i 26 (13638638521 t - 9734062522 t + 1) ) b(i) t = - -------------------------------------- / 2 ----- (t - 1) (t - 208211515202 t + 1) i = 0 infinity ----- 2 \ i 4 (84893504807 t - 110273248814 t + 7) ) c(i) t = --------------------------------------- / 2 ----- (t - 1) (t - 208211515202 t + 1) i = 0 In Maple notation, these generating functions are (300611646373*t^2+1053397696054*t-27)/(t-1)/(t^2-208211515202*t+1) -26*(13638638521*t^2-9734062522*t+1)/(t-1)/(t^2-208211515202*t+1) 4*(84893504807*t^2-110273248814*t+7)/(t-1)/(t^2-208211515202*t+1) Then for all i>=0 we have 3 3 3 a(i) + 5 b(i) + 5 c(i) = -2197 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 5, : Let a(i), b(i), c(i) be defined in terms of the followi\ ng generating functions infinity ----- \ i ) a(i) t = 30 ( / ----- i = 0 356674847355423726202060387307722572276259027253700443684060864032768511231 2 t + 636079449761723067519042389326072502645803687206823269321042649262753818370 / 2 t - 1) / ((t - 1) (t - 2706587653977154476086667731393471090083824099\ / 275402378583879792531106022402 t + 1)) infinity ----- \ i ) b(i) t = - 9 (1260256534854750294376290430829693761261183075503687\ / ----- i = 0 2 700927251510955326864323 t - 106938568592096439205676100050988560692463\ / 2 1768627887351100331722847314038726 t + 3) / ((t - 1) (t - 27065876539\ / 77154476086667731393471090083824099275402378583879792531106022402 t + 1)) infinity ----- \ i ) c(i) t = (10930760912898032965307313430573717806416502648086611873\ / ----- i = 0 2 325193370867824265949 t - 126485985533021060861830783034519911954454644\ / 2 09968815021767471463839939696378 t + 29) / ((t - 1) (t - 270658765397\ / 7154476086667731393471090083824099275402378583879792531106022402 t + 1)) In Maple notation, these generating functions are 30*(356674847355423726202060387307722572276259027253700443684060864032768511231 *t^2+ 636079449761723067519042389326072502645803687206823269321042649262753818370*t-1 )/(t-1)/(t^2-\ 2706587653977154476086667731393471090083824099275402378583879792531106022402*t+ 1) -9*( 1260256534854750294376290430829693761261183075503687700927251510955326864323*t^ 2-1069385685920964392056761000509885606924631768627887351100331722847314038726* t+3)/(t-1)/(t^2-\ 2706587653977154476086667731393471090083824099275402378583879792531106022402*t+ 1) (10930760912898032965307313430573717806416502648086611873325193370867824265949* t^2-\ 12648598553302106086183078303451991195445464409968815021767471463839939696378*t +29)/(t-1)/(t^2-\ 2706587653977154476086667731393471090083824099275402378583879792531106022402*t+ 1) Then for all i>=0 we have 3 3 3 a(i) + 8 b(i) + 8 c(i) = -10648 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 6, : Let a(i), b(i), c(i) be defined in terms of the followi\ ng generating functions infinity ----- \ i 2 ) a(i) t = (337902185594712926641271226827054443 t / ----- i = 0 / + 9254316909642222843821611531511910322 t - 29) / ((t - 1) / 2 (t - 3768371787414510481253275369347450434 t + 1)) infinity ----- \ i 2 ) b(i) t = - (164155935018615945193150811093351435 t / ----- i = 0 / + 3946795105797213670719513228194776306 t + 3) / ((t - 1) / 2 (t - 3768371787414510481253275369347450434 t + 1)) infinity ----- \ i 2 ) c(i) t = 2 (25760936576855818156363534408833311 t / ----- i = 0 / - 2081236456984770626112695554052897190 t + 7) / ((t - 1) / 2 (t - 3768371787414510481253275369347450434 t + 1)) In Maple notation, these generating functions are (337902185594712926641271226827054443*t^2+9254316909642222843821611531511910322 *t-29)/(t-1)/(t^2-3768371787414510481253275369347450434*t+1) -(164155935018615945193150811093351435*t^2+ 3946795105797213670719513228194776306*t+3)/(t-1)/(t^2-\ 3768371787414510481253275369347450434*t+1) 2*(25760936576855818156363534408833311*t^2-\ 2081236456984770626112695554052897190*t+7)/(t-1)/(t^2-\ 3768371787414510481253275369347450434*t+1) Then for all i>=0 we have 3 3 3 a(i) + 9 b(i) + 9 c(i) = -64 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 7, : Let a(i), b(i), c(i) be defined in terms of the followi\ ng generating functions infinity ----- 2 \ i 4 (233 t + 25118 t - 7) ) a(i) t = -------------------------- / 2 ----- (t - 1) (t - 64514 t + 1) i = 0 infinity ----- 2 \ i 433 t + 45646 t + 1 ) b(i) t = - -------------------------- / 2 ----- (t - 1) (t - 64514 t + 1) i = 0 infinity ----- 2 \ i 61 t - 46154 t + 13 ) c(i) t = -------------------------- / 2 ----- (t - 1) (t - 64514 t + 1) i = 0 In Maple notation, these generating functions are 4*(233*t^2+25118*t-7)/(t-1)/(t^2-64514*t+1) -(433*t^2+45646*t+1)/(t-1)/(t^2-64514*t+1) (61*t^2-46154*t+13)/(t-1)/(t^2-64514*t+1) Then for all i>=0 we have 3 3 3 a(i) + 10 b(i) + 10 c(i) = -8 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 8, : Let a(i), b(i), c(i) be defined in terms of the followi\ ng generating functions infinity ----- 2 \ i 1968551527 t + 3332897202 t - 25 ) a(i) t = --------------------------------- / 2 ----- (t - 1) (t - 554602498 t + 1) i = 0 infinity ----- 2 \ i 1224848651 t - 504898838 t + 11 ) b(i) t = - -------------------------------- / 2 ----- (t - 1) (t - 554602498 t + 1) i = 0 infinity ----- 2 \ i 1045889423 t - 1765839262 t + 15 ) c(i) t = --------------------------------- / 2 ----- (t - 1) (t - 554602498 t + 1) i = 0 In Maple notation, these generating functions are (1968551527*t^2+3332897202*t-25)/(t-1)/(t^2-554602498*t+1) -(1224848651*t^2-504898838*t+11)/(t-1)/(t^2-554602498*t+1) (1045889423*t^2-1765839262*t+15)/(t-1)/(t^2-554602498*t+1) Then for all i>=0 we have 3 3 3 a(i) + 11 b(i) + 11 c(i) = -6859 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 9, : Let a(i), b(i), c(i) be defined in terms of the followi\ ng generating functions infinity ----- 2 \ i 25 (2570447454546815 t + 10359722723965058 t - 1) ) a(i) t = -------------------------------------------------- / 2 ----- (t - 1) (t - 58468448039040002 t + 1) i = 0 infinity ----- 2 \ i 11 (3613322070240481 t + 47311198290718 t + 1) ) b(i) t = - ----------------------------------------------- / 2 ----- (t - 1) (t - 58468448039040002 t + 1) i = 0 infinity ----- 2 \ i 2 (17195721954503047 t - 37329204931424654 t + 7) ) c(i) t = -------------------------------------------------- / 2 ----- (t - 1) (t - 58468448039040002 t + 1) i = 0 In Maple notation, these generating functions are 25*(2570447454546815*t^2+10359722723965058*t-1)/(t-1)/(t^2-58468448039040002*t+ 1) -11*(3613322070240481*t^2+47311198290718*t+1)/(t-1)/(t^2-58468448039040002*t+1) 2*(17195721954503047*t^2-37329204931424654*t+7)/(t-1)/(t^2-58468448039040002*t+ 1) Then for all i>=0 we have 3 3 3 a(i) + 12 b(i) + 12 c(i) = -1331 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 10, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- \ i ) a(i) t = 30 / ----- i = 0 2 (91457757777101650995832887803 t + 760558022177257933677763959398 t - 1) / 2 / ((t - 1) (t - 5049846951510313885417026062402 t + 1)) / infinity ----- \ i ) b(i) t = - 4 / ----- i = 0 2 (303177880123027790782910447191 t + 1745161426479576416206353206008 t + 1) / 2 / ((t - 1) (t - 5049846951510313885417026062402 t + 1)) / infinity ----- \ i ) c(i) t = 13 / ----- i = 0 2 (44580186783776902550807002081 t - 674838434969193581624426587682 t + 1) / 2 / ((t - 1) (t - 5049846951510313885417026062402 t + 1)) / In Maple notation, these generating functions are 30*(91457757777101650995832887803*t^2+760558022177257933677763959398*t-1)/(t-1) /(t^2-5049846951510313885417026062402*t+1) -4*(303177880123027790782910447191*t^2+1745161426479576416206353206008*t+1)/(t-\ 1)/(t^2-5049846951510313885417026062402*t+1) 13*(44580186783776902550807002081*t^2-674838434969193581624426587682*t+1)/(t-1) /(t^2-5049846951510313885417026062402*t+1) Then for all i>=0 we have 3 3 3 a(i) + 13 b(i) + 13 c(i) = -729 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 11, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 4706277428522851 t + 10537895626211578 t - 29 ) a(i) t = ---------------------------------------------- / 2 ----- (t - 1) (t - 1572185782036802 t + 1) i = 0 infinity ----- 2 \ i 8 (292637212067341 t + 59829216943858 t + 1) ) b(i) t = - --------------------------------------------- / 2 ----- (t - 1) (t - 1572185782036802 t + 1) i = 0 infinity ----- 2 \ i 14 (125200929855241 t - 326610317861642 t + 1) ) c(i) t = ----------------------------------------------- / 2 ----- (t - 1) (t - 1572185782036802 t + 1) i = 0 In Maple notation, these generating functions are (4706277428522851*t^2+10537895626211578*t-29)/(t-1)/(t^2-1572185782036802*t+1) -8*(292637212067341*t^2+59829216943858*t+1)/(t-1)/(t^2-1572185782036802*t+1) 14*(125200929855241*t^2-326610317861642*t+1)/(t-1)/(t^2-1572185782036802*t+1) Then for all i>=0 we have 3 3 3 a(i) + 14 b(i) + 14 c(i) = -6859 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 12, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 88364999949336921211 t + 253012234560012001186 t - 29 ) a(i) t = ------------------------------------------------------ / 2 ----- (t - 1) (t - 42530229188456857154 t + 1) i = 0 infinity ----- 2 \ i 53934705541596771061 t - 19872675490774816514 t + 13 ) b(i) t = - ----------------------------------------------------- / 2 ----- (t - 1) (t - 42530229188456857154 t + 1) i = 0 infinity ----- 2 \ i 16 (3002731596560894353 t - 5131608474737266514 t + 1) ) c(i) t = ------------------------------------------------------- / 2 ----- (t - 1) (t - 42530229188456857154 t + 1) i = 0 In Maple notation, these generating functions are (88364999949336921211*t^2+253012234560012001186*t-29)/(t-1)/(t^2-\ 42530229188456857154*t+1) -(53934705541596771061*t^2-19872675490774816514*t+13)/(t-1)/(t^2-\ 42530229188456857154*t+1) 16*(3002731596560894353*t^2-5131608474737266514*t+1)/(t-1)/(t^2-\ 42530229188456857154*t+1) Then for all i>=0 we have 3 3 3 a(i) + 15 b(i) + 15 c(i) = -4096 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 13, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 2 (54560776049229139189 t + 292123958325286429462 t - 11) ) a(i) t = ---------------------------------------------------------- / 2 ----- (t - 1) (t - 115561578124838522882 t + 1) i = 0 infinity ----- 2 \ i 44140595050111976641 t + 186982561199565069118 t + 1 ) b(i) t = - ----------------------------------------------------- / 2 ----- (t - 1) (t - 115561578124838522882 t + 1) i = 0 infinity ----- 2 \ i 9 (1873356336166378561 t - 27553707030574939202 t + 1) ) c(i) t = ------------------------------------------------------- / 2 ----- (t - 1) (t - 115561578124838522882 t + 1) i = 0 In Maple notation, these generating functions are 2*(54560776049229139189*t^2+292123958325286429462*t-11)/(t-1)/(t^2-\ 115561578124838522882*t+1) -(44140595050111976641*t^2+186982561199565069118*t+1)/(t-1)/(t^2-\ 115561578124838522882*t+1) 9*(1873356336166378561*t^2-27553707030574939202*t+1)/(t-1)/(t^2-\ 115561578124838522882*t+1) Then for all i>=0 we have 3 3 3 a(i) + 16 b(i) + 16 c(i) = -1000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 14, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 30 (1499017295 t + 3282128306 t - 1) ) a(i) t = ------------------------------------- / 2 ----- (t - 1) (t - 12745958402 t + 1) i = 0 infinity ----- 2 \ i 4 (4695516841 t + 4372854358 t + 1) ) b(i) t = - ------------------------------------ / 2 ----- (t - 1) (t - 12745958402 t + 1) i = 0 infinity ----- 2 \ i 10846093453 t - 47119578266 t + 13 ) c(i) t = ----------------------------------- / 2 ----- (t - 1) (t - 12745958402 t + 1) i = 0 In Maple notation, these generating functions are 30*(1499017295*t^2+3282128306*t-1)/(t-1)/(t^2-12745958402*t+1) -4*(4695516841*t^2+4372854358*t+1)/(t-1)/(t^2-12745958402*t+1) (10846093453*t^2-47119578266*t+13)/(t-1)/(t^2-12745958402*t+1) Then for all i>=0 we have 3 3 3 a(i) + 17 b(i) + 17 c(i) = -9261 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 15, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 453851107 t + 981534778 t - 29 ) a(i) t = ------------------------------- / 2 ----- (t - 1) (t - 150945794 t + 1) i = 0 infinity ----- 2 \ i 16 (19498337 t - 13895010 t + 1) ) b(i) t = - --------------------------------- / 2 ----- (t - 1) (t - 150945794 t + 1) i = 0 infinity ----- 2 \ i 2 (146531465 t - 191358098 t + 9) ) c(i) t = ---------------------------------- / 2 ----- (t - 1) (t - 150945794 t + 1) i = 0 In Maple notation, these generating functions are (453851107*t^2+981534778*t-29)/(t-1)/(t^2-150945794*t+1) -16*(19498337*t^2-13895010*t+1)/(t-1)/(t^2-150945794*t+1) 2*(146531465*t^2-191358098*t+9)/(t-1)/(t^2-150945794*t+1) Then for all i>=0 we have 3 3 3 a(i) + 18 b(i) + 18 c(i) = -6859 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 16, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 16 (333473826479 t + 539402089154 t - 1) ) a(i) t = ----------------------------------------- / 2 ----- (t - 1) (t - 1773462177794 t + 1) i = 0 infinity ----- 2 \ i 2042688388297 t + 1836760125622 t + 1 ) b(i) t = - -------------------------------------- / 2 ----- (t - 1) (t - 1773462177794 t + 1) i = 0 infinity ----- 2 \ i 7 (139367449081 t - 693574379642 t + 1) ) c(i) t = ---------------------------------------- / 2 ----- (t - 1) (t - 1773462177794 t + 1) i = 0 In Maple notation, these generating functions are 16*(333473826479*t^2+539402089154*t-1)/(t-1)/(t^2-1773462177794*t+1) -(2042688388297*t^2+1836760125622*t+1)/(t-1)/(t^2-1773462177794*t+1) 7*(139367449081*t^2-693574379642*t+1)/(t-1)/(t^2-1773462177794*t+1) Then for all i>=0 we have 3 3 3 a(i) + 20 b(i) + 20 c(i) = -2744 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 17, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 15 (209598681599 t + 770591485442 t - 1) ) a(i) t = ----------------------------------------- / 2 ----- (t - 1) (t - 4194312192002 t + 1) i = 0 infinity ----- 2 \ i 7 (269451866881 t - 126390055682 t + 1) ) b(i) t = - ---------------------------------------- / 2 ----- (t - 1) (t - 4194312192002 t + 1) i = 0 infinity ----- 2 \ i 8 (217906859521 t - 343085944322 t + 1) ) c(i) t = ---------------------------------------- / 2 ----- (t - 1) (t - 4194312192002 t + 1) i = 0 In Maple notation, these generating functions are 15*(209598681599*t^2+770591485442*t-1)/(t-1)/(t^2-4194312192002*t+1) -7*(269451866881*t^2-126390055682*t+1)/(t-1)/(t^2-4194312192002*t+1) 8*(217906859521*t^2-343085944322*t+1)/(t-1)/(t^2-4194312192002*t+1) Then for all i>=0 we have 3 3 3 a(i) + 22 b(i) + 22 c(i) = -343 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 18, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 224882982617 t + 676318946102 t - 15 ) a(i) t = ------------------------------------- / 2 ----- (t - 1) (t - 224981359682 t + 1) i = 0 infinity ----- 2 \ i 7 (19242046825 t - 10853684074 t + 1) ) b(i) t = - -------------------------------------- / 2 ----- (t - 1) (t - 224981359682 t + 1) i = 0 infinity ----- 2 \ i 8 (15614600849 t - 22954418258 t + 1) ) c(i) t = -------------------------------------- / 2 ----- (t - 1) (t - 224981359682 t + 1) i = 0 In Maple notation, these generating functions are (224882982617*t^2+676318946102*t-15)/(t-1)/(t^2-224981359682*t+1) -7*(19242046825*t^2-10853684074*t+1)/(t-1)/(t^2-224981359682*t+1) 8*(15614600849*t^2-22954418258*t+1)/(t-1)/(t^2-224981359682*t+1) Then for all i>=0 we have 3 3 3 a(i) + 23 b(i) + 23 c(i) = -512 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 19, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 4 (177965393 t + 322952438 t - 7) ) a(i) t = ---------------------------------- / 2 ----- (t - 1) (t - 168844034 t + 1) i = 0 infinity ----- 2 \ i 3 (86599417 t + 65886982 t + 1) ) b(i) t = - -------------------------------- / 2 ----- (t - 1) (t - 168844034 t + 1) i = 0 infinity ----- 2 \ i 11 (13263673 t - 54850874 t + 1) ) c(i) t = --------------------------------- / 2 ----- (t - 1) (t - 168844034 t + 1) i = 0 In Maple notation, these generating functions are 4*(177965393*t^2+322952438*t-7)/(t-1)/(t^2-168844034*t+1) -3*(86599417*t^2+65886982*t+1)/(t-1)/(t^2-168844034*t+1) 11*(13263673*t^2-54850874*t+1)/(t-1)/(t^2-168844034*t+1) Then for all i>=0 we have 3 3 3 a(i) + 25 b(i) + 25 c(i) = -10648 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 20, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- \ i 2 ) a(i) t = (105965541278636145904869765804540056378569701203506343 t / ----- i = 0 / + 2139755322541384080424244447915215073385012965044783538 t - 25) / ( / (t - 1) 2 (t - 1486558061832258582898307377598314512810496324230369602 t + 1)) infinity ----- \ i 2 ) b(i) t = - 9 (5402729394234243631717070275088280741386021845573321 t / ----- i = 0 / + 21205981118927645158060851734890682227642040213710006 t + 1) / ( / (t - 1) 2 (t - 1486558061832258582898307377598314512810496324230369602 t + 1)) infinity ----- \ i 2 ) c(i) t = (41055597313919896549391506346898808359719217952766579 t / ----- i = 0 / - 280533991932376895657392804436709475080971776486316542 t + 11) / ( / (t - 1) 2 (t - 1486558061832258582898307377598314512810496324230369602 t + 1)) In Maple notation, these generating functions are (105965541278636145904869765804540056378569701203506343*t^2+ 2139755322541384080424244447915215073385012965044783538*t-25)/(t-1)/(t^2-\ 1486558061832258582898307377598314512810496324230369602*t+1) -9*(5402729394234243631717070275088280741386021845573321*t^2+ 21205981118927645158060851734890682227642040213710006*t+1)/(t-1)/(t^2-\ 1486558061832258582898307377598314512810496324230369602*t+1) (41055597313919896549391506346898808359719217952766579*t^2-\ 280533991932376895657392804436709475080971776486316542*t+11)/(t-1)/(t^2-\ 1486558061832258582898307377598314512810496324230369602*t+1) Then for all i>=0 we have 3 3 3 a(i) + 26 b(i) + 26 c(i) = -27 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 21, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- \ i ) a(i) t = 30 ( / ----- i = 0 52525439129546180621123145257183145612249802432350468785468641727795871695 2 t + 353601318782013871355691627002096657764957671665136504716619159165826899506 / 2 t - 1) / ((t - 1) (t - 2706587653977154476086667731393471090083824099\ / 275402378583879792531106022402 t + 1)) infinity ----- \ i ) b(i) t = - 18 ( / ----- i = 0 61863560420118111719835877579407568162220101157547138968549025309606048721 2 t - 35835717383692761403536409808524638025417650219938000355787236022149754322 / 2 t + 1) / ((t - 1) (t - 2706587653977154476086667731393471090083824099\ / 275402378583879792531106022402 t + 1)) infinity ----- \ i ) c(i) t = (10731399036163212566331049154622722687566927420417327562\ / ----- i = 0 2 14291192705373591059 t - 1541641078271977562326495335338165011219136858\ / 2 918697251244003399879586890278 t + 19) / ((t - 1) (t - 27065876539771\ / 54476086667731393471090083824099275402378583879792531106022402 t + 1)) In Maple notation, these generating functions are 30*(52525439129546180621123145257183145612249802432350468785468641727795871695* t^2+353601318782013871355691627002096657764957671665136504716619159165826899506 *t-1)/(t-1)/(t^2-\ 2706587653977154476086667731393471090083824099275402378583879792531106022402*t+ 1) -18*(61863560420118111719835877579407568162220101157547138968549025309606048721 *t^2-35835717383692761403536409808524638025417650219938000355787236022149754322 *t+1)/(t-1)/(t^2-\ 2706587653977154476086667731393471090083824099275402378583879792531106022402*t+ 1) (1073139903616321256633104915462272268756692742041732756214291192705373591059*t ^2-1541641078271977562326495335338165011219136858918697251244003399879586890278 *t+19)/(t-1)/(t^2-\ 2706587653977154476086667731393471090083824099275402378583879792531106022402*t+ 1) Then for all i>=0 we have 3 3 3 a(i) + 27 b(i) + 27 c(i) = -729 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 22, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- \ i ) a(i) t = 19 / ----- i = 0 2 (5984925327852809112355409159 t + 18351998965852720076416734842 t - 1) / 2 / ((t - 1) (t - 92397887795300190051988929602 t + 1)) / infinity ----- \ i ) b(i) t = / ----- i = 0 2 9 (7511487431579847201481390841 t - 4855586206420063762579934842 t + 1) - ------------------------------------------------------------------------ 2 (t - 1) (t - 92397887795300190051988929602 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 10 (6368222891079781884316862881 t - 8758533993723586979328173282 t + 1) ------------------------------------------------------------------------- 2 (t - 1) (t - 92397887795300190051988929602 t + 1) In Maple notation, these generating functions are 19*(5984925327852809112355409159*t^2+18351998965852720076416734842*t-1)/(t-1)/( t^2-92397887795300190051988929602*t+1) -9*(7511487431579847201481390841*t^2-4855586206420063762579934842*t+1)/(t-1)/(t ^2-92397887795300190051988929602*t+1) 10*(6368222891079781884316862881*t^2-8758533993723586979328173282*t+1)/(t-1)/(t ^2-92397887795300190051988929602*t+1) Then for all i>=0 we have 3 3 3 a(i) + 29 b(i) + 29 c(i) = -1000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 23, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- \ i 2 ) a(i) t = 27 (6782930439203796854220568905479447852399 t / ----- i = 0 / + 153084082805155399656975303681727157528402 t - 1) / ((t - 1) / 2 (t - 2813816937547268025293117501251670941012802 t + 1)) infinity ----- \ i 2 ) b(i) t = - (69973975293913189994137926695000723545567 t / ----- i = 0 / + 567919033218061929089944126485478834870426 t + 7) / ((t - 1) / 2 (t - 2813816937547268025293117501251670941012802 t + 1)) infinity ----- \ i 2 ) c(i) t = 10 (5166006310806293848774239065020621434409 t / ----- i = 0 / - 68955307162003805757182444383068577276010 t + 1) / ((t - 1) / 2 (t - 2813816937547268025293117501251670941012802 t + 1)) In Maple notation, these generating functions are 27*(6782930439203796854220568905479447852399*t^2+ 153084082805155399656975303681727157528402*t-1)/(t-1)/(t^2-\ 2813816937547268025293117501251670941012802*t+1) -(69973975293913189994137926695000723545567*t^2+ 567919033218061929089944126485478834870426*t+7)/(t-1)/(t^2-\ 2813816937547268025293117501251670941012802*t+1) 10*(5166006310806293848774239065020621434409*t^2-\ 68955307162003805757182444383068577276010*t+1)/(t-1)/(t^2-\ 2813816937547268025293117501251670941012802*t+1) Then for all i>=0 we have 3 3 3 a(i) + 30 b(i) + 30 c(i) = -27 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 24, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- \ i 2 ) a(i) t = (562462931879306805070821340181944871750123765368099 t / ----- i = 0 / + 3208567677719283234139156254959297475996735305095930 t - 29) / ( / 2 (t - 1) (t - 746280566062256564369757600014731282242242822148098 t + 1)) infinity ----- \ i 2 ) b(i) t = - 8 (28944326420206982082611897019631603894003193782129 t / ----- i = 0 / + 25064501802010112546751341419255680577964533582990 t + 1) / ((t - 1) / 2 (t - 746280566062256564369757600014731282242242822148098 t + 1)) infinity ----- \ i 2 ) c(i) t = 11 (17117111998756778542103608040977216316267191524289 t / ----- i = 0 / - 56396259796732847363458690541986150477698265971650 t + 1) / ((t - 1) / 2 (t - 746280566062256564369757600014731282242242822148098 t + 1)) In Maple notation, these generating functions are (562462931879306805070821340181944871750123765368099*t^2+ 3208567677719283234139156254959297475996735305095930*t-29)/(t-1)/(t^2-\ 746280566062256564369757600014731282242242822148098*t+1) -8*(28944326420206982082611897019631603894003193782129*t^2+ 25064501802010112546751341419255680577964533582990*t+1)/(t-1)/(t^2-\ 746280566062256564369757600014731282242242822148098*t+1) 11*(17117111998756778542103608040977216316267191524289*t^2-\ 56396259796732847363458690541986150477698265971650*t+1)/(t-1)/(t^2-\ 746280566062256564369757600014731282242242822148098*t+1) Then for all i>=0 we have 3 3 3 a(i) + 31 b(i) + 31 c(i) = -1000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 25, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- \ i ) a(i) t = 4 ( / ----- i = 0 2 7390009139138677749357805646183269858628917745920765407034720889 t + 64385338972674604980520703571453686334248505098079208216165199246 t - 7) / 2 / ((t - 1) (t / - 64350312100246391412994525505467615897062517032551700489765445634 t + 1) ) infinity ----- \ i ) b(i) t = - 3 ( / ----- i = 0 2 3238400775343190651658547702996782810383262134996981548631619265 t + 19036707259357483298993403433511238077061455299347837851671804222 t + 1) / 2 / ((t - 1) (t / - 64350312100246391412994525505467615897062517032551700489765445634 t + 1) ) infinity ----- \ i ) c(i) t = 9 ( / ----- i = 0 2 532058840733754087637456223503870576895982360115974189763523393 t - 7957094852300645404521439935673210872710888171564247323197997890 t + 1) / 2 / ((t - 1) (t / - 64350312100246391412994525505467615897062517032551700489765445634 t + 1) ) In Maple notation, these generating functions are 4*(7390009139138677749357805646183269858628917745920765407034720889*t^2+ 64385338972674604980520703571453686334248505098079208216165199246*t-7)/(t-1)/(t ^2-64350312100246391412994525505467615897062517032551700489765445634*t+1) -3*(3238400775343190651658547702996782810383262134996981548631619265*t^2+ 19036707259357483298993403433511238077061455299347837851671804222*t+1)/(t-1)/(t ^2-64350312100246391412994525505467615897062517032551700489765445634*t+1) 9*(532058840733754087637456223503870576895982360115974189763523393*t^2-\ 7957094852300645404521439935673210872710888171564247323197997890*t+1)/(t-1)/(t^ 2-64350312100246391412994525505467615897062517032551700489765445634*t+1) Then for all i>=0 we have 3 3 3 a(i) + 32 b(i) + 32 c(i) = -512 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 26, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 30 (26914928482000734455543 t + 677293786149228542731658 t - 1) ---------------------------------------------------------------- 2 (t - 1) (t - 13825485377045766625593602 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 8 (38127002885359452099871 t + 317570256035516560356928 t + 1) - --------------------------------------------------------------- 2 (t - 1) (t - 13825485377045766625593602 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 231611672677419068283851 t - 3077189744044427167938262 t + 11 -------------------------------------------------------------- 2 (t - 1) (t - 13825485377045766625593602 t + 1) In Maple notation, these generating functions are 30*(26914928482000734455543*t^2+677293786149228542731658*t-1)/(t-1)/(t^2-\ 13825485377045766625593602*t+1) -8*(38127002885359452099871*t^2+317570256035516560356928*t+1)/(t-1)/(t^2-\ 13825485377045766625593602*t+1) (231611672677419068283851*t^2-3077189744044427167938262*t+11)/(t-1)/(t^2-\ 13825485377045766625593602*t+1) Then for all i>=0 we have 3 3 3 a(i) + 33 b(i) + 33 c(i) = -27 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 27, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- \ i 2 ) a(i) t = (486785344140834328758044997338338259 t / ----- i = 0 / + 6445790806791122564305519299302320650 t - 29) / ((t - 1) / 2 (t - 2771232126740893793050830760343256898 t + 1)) infinity ----- \ i 2 ) b(i) t = - 5 (57634773190374847023291040699905179 t / ----- i = 0 / + 3508570293849934912937541942321122 t + 3) / ((t - 1) / 2 (t - 2771232126740893793050830760343256898 t + 1)) infinity ----- \ i 2 ) c(i) t = 16 (17116040621733253061032043973613129 t / ----- i = 0 / - 36223335460553497416103476049308850 t + 1) / ((t - 1) / 2 (t - 2771232126740893793050830760343256898 t + 1)) In Maple notation, these generating functions are (486785344140834328758044997338338259*t^2+6445790806791122564305519299302320650 *t-29)/(t-1)/(t^2-2771232126740893793050830760343256898*t+1) -5*(57634773190374847023291040699905179*t^2+3508570293849934912937541942321122* t+3)/(t-1)/(t^2-2771232126740893793050830760343256898*t+1) 16*(17116040621733253061032043973613129*t^2-36223335460553497416103476049308850 *t+1)/(t-1)/(t^2-2771232126740893793050830760343256898*t+1) Then for all i>=0 we have 3 3 3 a(i) + 34 b(i) + 34 c(i) = -125 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 28, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 4 (643703273 t + 3642600734 t - 7) ) a(i) t = ----------------------------------- / 2 ----- (t - 1) (t - 3317529602 t + 1) i = 0 infinity ----- 2 \ i 5 (174934321 t + 354755278 t + 1) ) b(i) t = - ---------------------------------- / 2 ----- (t - 1) (t - 3317529602 t + 1) i = 0 infinity ----- 2 \ i 9 (67070961 t - 361342962 t + 1) ) c(i) t = --------------------------------- / 2 ----- (t - 1) (t - 3317529602 t + 1) i = 0 In Maple notation, these generating functions are 4*(643703273*t^2+3642600734*t-7)/(t-1)/(t^2-3317529602*t+1) -5*(174934321*t^2+354755278*t+1)/(t-1)/(t^2-3317529602*t+1) 9*(67070961*t^2-361342962*t+1)/(t-1)/(t^2-3317529602*t+1) Then for all i>=0 we have 3 3 3 a(i) + 38 b(i) + 38 c(i) = -1000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 29, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 300611646373 t + 1053397696054 t - 27 ) a(i) t = -------------------------------------- / 2 ----- (t - 1) (t - 208211515202 t + 1) i = 0 infinity ----- 2 \ i 13 (13638638521 t - 9734062522 t + 1) ) b(i) t = - -------------------------------------- / 2 ----- (t - 1) (t - 208211515202 t + 1) i = 0 infinity ----- 2 \ i 2 (84893504807 t - 110273248814 t + 7) ) c(i) t = --------------------------------------- / 2 ----- (t - 1) (t - 208211515202 t + 1) i = 0 In Maple notation, these generating functions are (300611646373*t^2+1053397696054*t-27)/(t-1)/(t^2-208211515202*t+1) -13*(13638638521*t^2-9734062522*t+1)/(t-1)/(t^2-208211515202*t+1) 2*(84893504807*t^2-110273248814*t+7)/(t-1)/(t^2-208211515202*t+1) Then for all i>=0 we have 3 3 3 a(i) + 40 b(i) + 40 c(i) = -2197 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 30, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 495718603330829 t + 1553892614955662 t - 27 ) a(i) t = -------------------------------------------- / 2 ----- (t - 1) (t - 292671004216898 t + 1) i = 0 infinity ----- 2 \ i 292227334887029 t - 217263855895298 t + 13 ) b(i) t = - ------------------------------------------- / 2 ----- (t - 1) (t - 292671004216898 t + 1) i = 0 infinity ----- 2 \ i 14 (20009759803201 t - 25364294016898 t + 1) ) c(i) t = --------------------------------------------- / 2 ----- (t - 1) (t - 292671004216898 t + 1) i = 0 In Maple notation, these generating functions are (495718603330829*t^2+1553892614955662*t-27)/(t-1)/(t^2-292671004216898*t+1) -(292227334887029*t^2-217263855895298*t+13)/(t-1)/(t^2-292671004216898*t+1) 14*(20009759803201*t^2-25364294016898*t+1)/(t-1)/(t^2-292671004216898*t+1) Then for all i>=0 we have 3 3 3 a(i) + 41 b(i) + 41 c(i) = -2744 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 31, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 23 (183753291628320422399 t + 653846114513254017602 t - 1) ) a(i) t = ----------------------------------------------------------- / 2 ----- (t - 1) (t - 2569888732962123720002 t + 1) i = 0 infinity ----- 2 \ i 1251758402892297595801 t + 3137686586254687444198 t + 1 ) b(i) t = - -------------------------------------------------------- / 2 ----- (t - 1) (t - 2569888732962123720002 t + 1) i = 0 infinity ----- 2 \ i 547370784983735976607 t - 4936815774130721016614 t + 7 ) c(i) t = ------------------------------------------------------- / 2 ----- (t - 1) (t - 2569888732962123720002 t + 1) i = 0 In Maple notation, these generating functions are 23*(183753291628320422399*t^2+653846114513254017602*t-1)/(t-1)/(t^2-\ 2569888732962123720002*t+1) -(1251758402892297595801*t^2+3137686586254687444198*t+1)/(t-1)/(t^2-\ 2569888732962123720002*t+1) (547370784983735976607*t^2-4936815774130721016614*t+7)/(t-1)/(t^2-\ 2569888732962123720002*t+1) Then for all i>=0 we have 3 3 3 a(i) + 42 b(i) + 42 c(i) = -2197 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 32, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 34170734659189817699 t + 119257364945018568378 t - 29 ) a(i) t = ------------------------------------------------------ / 2 ----- (t - 1) (t - 21909411743967887362 t + 1) i = 0 infinity ----- 2 \ i 14 (1437463086158381569 t - 1055270508068880898 t + 1) ) b(i) t = - ------------------------------------------------------- / 2 ----- (t - 1) (t - 21909411743967887362 t + 1) i = 0 infinity ----- 2 \ i 19329814958329206671 t - 24680511051582216094 t + 15 ) c(i) t = ----------------------------------------------------- / 2 ----- (t - 1) (t - 21909411743967887362 t + 1) i = 0 In Maple notation, these generating functions are (34170734659189817699*t^2+119257364945018568378*t-29)/(t-1)/(t^2-\ 21909411743967887362*t+1) -14*(1437463086158381569*t^2-1055270508068880898*t+1)/(t-1)/(t^2-\ 21909411743967887362*t+1) (19329814958329206671*t^2-24680511051582216094*t+15)/(t-1)/(t^2-\ 21909411743967887362*t+1) Then for all i>=0 we have 3 3 3 a(i) + 43 b(i) + 43 c(i) = -2744 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 33, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 29 (664027824650231569439 t + 2089094283818714326562 t - 1) ) a(i) t = ------------------------------------------------------------ / 2 ----- (t - 1) (t - 10641282555992364129602 t + 1) i = 0 infinity ----- \ i ) b(i) t = / ----- i = 0 2 2 (5668016071537089913927 t - 4307449142642289385934 t + 7) - ------------------------------------------------------------ 2 (t - 1) (t - 10641282555992364129602 t + 1) infinity ----- 2 \ i 15 (726558496030919995321 t - 907967419883560065722 t + 1) ) c(i) t = ----------------------------------------------------------- / 2 ----- (t - 1) (t - 10641282555992364129602 t + 1) i = 0 In Maple notation, these generating functions are 29*(664027824650231569439*t^2+2089094283818714326562*t-1)/(t-1)/(t^2-\ 10641282555992364129602*t+1) -2*(5668016071537089913927*t^2-4307449142642289385934*t+7)/(t-1)/(t^2-\ 10641282555992364129602*t+1) 15*(726558496030919995321*t^2-907967419883560065722*t+1)/(t-1)/(t^2-\ 10641282555992364129602*t+1) Then for all i>=0 we have 3 3 3 a(i) + 44 b(i) + 44 c(i) = -3375 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 34, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 2 (9893 t + 352514 t - 7) ) a(i) t = ---------------------------- / 2 ----- (t - 1) (t - 1435202 t + 1) i = 0 infinity ----- 2 \ i 4 (1811 t + 16188 t + 1) ) b(i) t = - ---------------------------- / 2 ----- (t - 1) (t - 1435202 t + 1) i = 0 infinity ----- 2 \ i 5 (1185 t - 15586 t + 1) ) c(i) t = ---------------------------- / 2 ----- (t - 1) (t - 1435202 t + 1) i = 0 In Maple notation, these generating functions are 2*(9893*t^2+352514*t-7)/(t-1)/(t^2-1435202*t+1) -4*(1811*t^2+16188*t+1)/(t-1)/(t^2-1435202*t+1) 5*(1185*t^2-15586*t+1)/(t-1)/(t^2-1435202*t+1) Then for all i>=0 we have 3 3 3 a(i) + 45 b(i) + 45 c(i) = -1 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 35, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 4 (186166199376425 t + 431792442054878 t - 7) ) a(i) t = ---------------------------------------------- / 2 ----- (t - 1) (t - 268510893235202 t + 1) i = 0 infinity ----- 2 \ i 246528672098549 t + 71081355899654 t + 5 ) b(i) t = - ----------------------------------------- / 2 ----- (t - 1) (t - 268510893235202 t + 1) i = 0 infinity ----- 2 \ i 9 (20197245716209 t - 55487248827122 t + 1) ) c(i) t = -------------------------------------------- / 2 ----- (t - 1) (t - 268510893235202 t + 1) i = 0 In Maple notation, these generating functions are 4*(186166199376425*t^2+431792442054878*t-7)/(t-1)/(t^2-268510893235202*t+1) -(246528672098549*t^2+71081355899654*t+5)/(t-1)/(t^2-268510893235202*t+1) 9*(20197245716209*t^2-55487248827122*t+1)/(t-1)/(t^2-268510893235202*t+1) Then for all i>=0 we have 3 3 3 a(i) + 46 b(i) + 46 c(i) = -5832 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 36, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 2 (3949215310643 t + 19766754834650 t - 13) ) a(i) t = -------------------------------------------- / 2 ----- (t - 1) (t - 9291462276098 t + 1) i = 0 infinity ----- 2 \ i 5 (520250211937 t + 649304480158 t + 1) ) b(i) t = - ---------------------------------------- / 2 ----- (t - 1) (t - 9291462276098 t + 1) i = 0 infinity ----- 2 \ i 8 (242881063489 t - 973852746050 t + 1) ) c(i) t = ---------------------------------------- / 2 ----- (t - 1) (t - 9291462276098 t + 1) i = 0 In Maple notation, these generating functions are 2*(3949215310643*t^2+19766754834650*t-13)/(t-1)/(t^2-9291462276098*t+1) -5*(520250211937*t^2+649304480158*t+1)/(t-1)/(t^2-9291462276098*t+1) 8*(242881063489*t^2-973852746050*t+1)/(t-1)/(t^2-9291462276098*t+1) Then for all i>=0 we have 3 3 3 a(i) + 48 b(i) + 48 c(i) = -1000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 37, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- \ i ) a(i) t = 27 ( / ----- i = 0 2 347217810101271112482506831836311056576438175616279026690108646026303 t + 443072526809066606279728119380604085872814070988082835216639137256386 t / 2 - 1) / ((t - 1) (t / - 1764380986686440298536082635279244499396706231285168468374854076403714 t + 1)) infinity ----- \ i ) b(i) t = - ( / ----- i = 0 2 3396634567835829044285249819266915196071700735894932368777865381134919 t - 1523605662628367703948593144868133524552560729743114324293198087537230 t / 2 + 7) / ((t - 1) (t / - 1764380986686440298536082635279244499396706231285168468374854076403714 t + 1)) infinity ----- \ i ) c(i) t = 2 ( / ----- i = 0 2 1422585493543375697524163601998739994283972993193362251429140530487749 t - 2359099946147106367692491939198130830043542996269271273671474177286602 t / 2 + 5) / ((t - 1) (t / - 1764380986686440298536082635279244499396706231285168468374854076403714 t + 1)) In Maple notation, these generating functions are 27*(347217810101271112482506831836311056576438175616279026690108646026303*t^2+ 443072526809066606279728119380604085872814070988082835216639137256386*t-1)/(t-1 )/(t^2-1764380986686440298536082635279244499396706231285168468374854076403714*t +1) -(3396634567835829044285249819266915196071700735894932368777865381134919*t^2-\ 1523605662628367703948593144868133524552560729743114324293198087537230*t+7)/(t-\ 1)/(t^2-1764380986686440298536082635279244499396706231285168468374854076403714* t+1) 2*(1422585493543375697524163601998739994283972993193362251429140530487749*t^2-\ 2359099946147106367692491939198130830043542996269271273671474177286602*t+5)/(t-\ 1)/(t^2-1764380986686440298536082635279244499396706231285168468374854076403714* t+1) Then for all i>=0 we have 3 3 3 a(i) + 51 b(i) + 51 c(i) = -13824 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 38, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 16 (60697328639 t + 146145297362 t - 1) ) a(i) t = ---------------------------------------- / 2 ----- (t - 1) (t - 650284185602 t + 1) i = 0 infinity ----- 2 \ i 3 (105623496361 t + 20175527638 t + 1) ) b(i) t = - --------------------------------------- / 2 ----- (t - 1) (t - 650284185602 t + 1) i = 0 infinity ----- 2 \ i 5 (48433216921 t - 123912631322 t + 1) ) c(i) t = --------------------------------------- / 2 ----- (t - 1) (t - 650284185602 t + 1) i = 0 In Maple notation, these generating functions are 16*(60697328639*t^2+146145297362*t-1)/(t-1)/(t^2-650284185602*t+1) -3*(105623496361*t^2+20175527638*t+1)/(t-1)/(t^2-650284185602*t+1) 5*(48433216921*t^2-123912631322*t+1)/(t-1)/(t^2-650284185602*t+1) Then for all i>=0 we have 3 3 3 a(i) + 52 b(i) + 52 c(i) = -1000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 39, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- \ i 2 ) a(i) t = (192649945605865298058996107152238954599099 t / ----- i = 0 / + 276819724713637908731191157615487529460578 t - 29) / ((t - 1) / 2 (t - 39112028727232147833895072667626260962882 t + 1)) infinity ----- \ i 2 ) b(i) t = - 3 (37679666867485547911037242061739382234733 t / ----- i = 0 / - 33251495924802922895931364675604927054962 t + 5) / ((t - 1) / 2 (t - 39112028727232147833895072667626260962882 t + 1)) infinity ----- \ i 2 ) c(i) t = 16 (6837755998023982098815949741349437288589 t / ----- i = 0 / - 7668038049776974289148301751249647634798 t + 1) / ((t - 1) / 2 (t - 39112028727232147833895072667626260962882 t + 1)) In Maple notation, these generating functions are (192649945605865298058996107152238954599099*t^2+ 276819724713637908731191157615487529460578*t-29)/(t-1)/(t^2-\ 39112028727232147833895072667626260962882*t+1) -3*(37679666867485547911037242061739382234733*t^2-\ 33251495924802922895931364675604927054962*t+5)/(t-1)/(t^2-\ 39112028727232147833895072667626260962882*t+1) 16*(6837755998023982098815949741349437288589*t^2-\ 7668038049776974289148301751249647634798*t+1)/(t-1)/(t^2-\ 39112028727232147833895072667626260962882*t+1) Then for all i>=0 we have 3 3 3 a(i) + 53 b(i) + 53 c(i) = -13824 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 40, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 11290733 t + 14207654 t - 19 ) a(i) t = ----------------------------- / 2 ----- (t - 1) (t - 2979074 t + 1) i = 0 infinity ----- 2 \ i 4072853 t - 1957786 t + 5 ) b(i) t = - ---------------------------- / 2 ----- (t - 1) (t - 2979074 t + 1) i = 0 infinity ----- 2 \ i 3445591 t - 5560670 t + 7 ) c(i) t = ---------------------------- / 2 ----- (t - 1) (t - 2979074 t + 1) i = 0 In Maple notation, these generating functions are (11290733*t^2+14207654*t-19)/(t-1)/(t^2-2979074*t+1) -(4072853*t^2-1957786*t+5)/(t-1)/(t^2-2979074*t+1) (3445591*t^2-5560670*t+7)/(t-1)/(t^2-2979074*t+1) Then for all i>=0 we have 3 3 3 a(i) + 54 b(i) + 54 c(i) = -4913 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 41, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 2 (5202955955 t + 12791689562 t - 13) ) a(i) t = -------------------------------------- / 2 ----- (t - 1) (t - 4430499842 t + 1) i = 0 infinity ----- 2 \ i 3367894853 t + 449151158 t + 5 ) b(i) t = - ------------------------------- / 2 ----- (t - 1) (t - 4430499842 t + 1) i = 0 infinity ----- 2 \ i 8 (328076929 t - 805207682 t + 1) ) c(i) t = ---------------------------------- / 2 ----- (t - 1) (t - 4430499842 t + 1) i = 0 In Maple notation, these generating functions are 2*(5202955955*t^2+12791689562*t-13)/(t-1)/(t^2-4430499842*t+1) -(3367894853*t^2+449151158*t+5)/(t-1)/(t^2-4430499842*t+1) 8*(328076929*t^2-805207682*t+1)/(t-1)/(t^2-4430499842*t+1) Then for all i>=0 we have 3 3 3 a(i) + 56 b(i) + 56 c(i) = -4096 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 42, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- \ i 2 ) a(i) t = 30 (571218282753456460043978046286170240470904519059 t / ----- i = 0 / + 709882998729698709075183922203831435997242380942 t - 1) / ((t - 1) / 2 (t - 2829221374126017775786532408573321710023907560002 t + 1)) infinity ----- \ i 2 ) b(i) t = - 8 (769650979583425194990941451926043676248779333326 t / ----- i = 0 / - 391946981077184619267878181905715595772825678327 t + 1) / ((t - 1) / 2 (t - 2829221374126017775786532408573321710023907560002 t + 1)) infinity ----- \ i 2 ) c(i) t = 11 (477753112029076248025376838775949911845393890401 t / ----- i = 0 / - 752446929124523939460331944245279424918814730402 t + 1) / ((t - 1) / 2 (t - 2829221374126017775786532408573321710023907560002 t + 1)) In Maple notation, these generating functions are 30*(571218282753456460043978046286170240470904519059*t^2+ 709882998729698709075183922203831435997242380942*t-1)/(t-1)/(t^2-\ 2829221374126017775786532408573321710023907560002*t+1) -8*(769650979583425194990941451926043676248779333326*t^2-\ 391946981077184619267878181905715595772825678327*t+1)/(t-1)/(t^2-\ 2829221374126017775786532408573321710023907560002*t+1) 11*(477753112029076248025376838775949911845393890401*t^2-\ 752446929124523939460331944245279424918814730402*t+1)/(t-1)/(t^2-\ 2829221374126017775786532408573321710023907560002*t+1) Then for all i>=0 we have 3 3 3 a(i) + 57 b(i) + 57 c(i) = -19683 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 43, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- \ i ) a(i) t = ( / ----- i = 0 2 27916049656715793217285189905003497454654421004202285302371 t / + 70866617073548241503578556038485175018025687581599358603258 t - 29) / / ((t - 1) 2 (t - 9507723956882057427335242776183411046367291637656395502402 t + 1)) infinity ----- \ i ) b(i) t = - 2 ( / ----- i = 0 2 3722982150787472722816570530295165596280686826220386099801 t / + 5009187283931999959690721928797755727271145976944400101798 t + 1) / ( / (t - 1) 2 (t - 9507723956882057427335242776183411046367291637656395502402 t + 1)) infinity ----- \ i ) c(i) t = 8 ( / ----- i = 0 2 494557261810683911684061540308111751341196378364435817101 t / - 2677599620490552082310884655081342082229154579155632367502 t + 1) / ( / (t - 1) 2 (t - 9507723956882057427335242776183411046367291637656395502402 t + 1)) In Maple notation, these generating functions are (27916049656715793217285189905003497454654421004202285302371*t^2+ 70866617073548241503578556038485175018025687581599358603258*t-29)/(t-1)/(t^2-\ 9507723956882057427335242776183411046367291637656395502402*t+1) -2*(3722982150787472722816570530295165596280686826220386099801*t^2+ 5009187283931999959690721928797755727271145976944400101798*t+1)/(t-1)/(t^2-\ 9507723956882057427335242776183411046367291637656395502402*t+1) 8*(494557261810683911684061540308111751341196378364435817101*t^2-\ 2677599620490552082310884655081342082229154579155632367502*t+1)/(t-1)/(t^2-\ 9507723956882057427335242776183411046367291637656395502402*t+1) Then for all i>=0 we have 3 3 3 a(i) + 62 b(i) + 62 c(i) = -6859 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 44, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- \ i ) a(i) t = 2 / ----- i = 0 2 (1949311402855681465823325251 t + 145990364812460127718295141834 t - 13) / 2 / ((t - 1) (t - 554992631482309011968823124994 t + 1)) / infinity ----- \ i ) b(i) t = / ----- i = 0 2 4 (264524756240471495595187465 t + 11553141686994815036863980022 t + 1) - ------------------------------------------------------------------------ 2 (t - 1) (t - 554992631482309011968823124994 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 624918713216178989975566471 t - 47895584486157325119812236430 t + 7 -------------------------------------------------------------------- 2 (t - 1) (t - 554992631482309011968823124994 t + 1) In Maple notation, these generating functions are 2*(1949311402855681465823325251*t^2+145990364812460127718295141834*t-13)/(t-1)/ (t^2-554992631482309011968823124994*t+1) -4*(264524756240471495595187465*t^2+11553141686994815036863980022*t+1)/(t-1)/(t ^2-554992631482309011968823124994*t+1) (624918713216178989975566471*t^2-47895584486157325119812236430*t+7)/(t-1)/(t^2-\ 554992631482309011968823124994*t+1) Then for all i>=0 we have 3 3 3 a(i) + 63 b(i) + 63 c(i) = -1 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 45, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- \ i 2 ) a(i) t = 24 (1100143005163055345549324256897794113961663 t / ----- i = 0 / + 15190662214472314348249103640666588447662402 t - 1) / ((t - 1) / 2 (t - 195062829311092505241900826616251253205123074 t + 1)) infinity ----- \ i 2 ) b(i) t = - 8 (1318848978506378412714910360902368388699697 t / ----- i = 0 / + 1295505134251699474826977085540824009290190 t + 1) / ((t - 1) / 2 (t - 195062829311092505241900826616251253205123074 t + 1)) infinity ----- \ i 2 ) c(i) t = 9 (1067534678815537445059349756653108969577985 t / ----- i = 0 / - 3391405001267162233985471931269279990013442 t + 1) / ((t - 1) / 2 (t - 195062829311092505241900826616251253205123074 t + 1)) In Maple notation, these generating functions are 24*(1100143005163055345549324256897794113961663*t^2+ 15190662214472314348249103640666588447662402*t-1)/(t-1)/(t^2-\ 195062829311092505241900826616251253205123074*t+1) -8*(1318848978506378412714910360902368388699697*t^2+ 1295505134251699474826977085540824009290190*t+1)/(t-1)/(t^2-\ 195062829311092505241900826616251253205123074*t+1) 9*(1067534678815537445059349756653108969577985*t^2-\ 3391405001267162233985471931269279990013442*t+1)/(t-1)/(t^2-\ 195062829311092505241900826616251253205123074*t+1) Then for all i>=0 we have 3 3 3 a(i) + 64 b(i) + 64 c(i) = -64 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 46, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- \ i 2 ) a(i) t = 8 (11261604924439579270269139914681681294523 t / ----- i = 0 / + 93364757732113000857480347698311098764399 t - 2) / ((t - 1) / 2 (t - 290119316370360939318381049317302688928322 t + 1)) infinity ----- \ i 2 ) b(i) t = - (22832394208315801538762109257964240693121 t / ----- i = 0 / + 140568140299128865433659401277068308243518 t + 1) / ((t - 1) / 2 (t - 290119316370360939318381049317302688928322 t + 1)) infinity ----- \ i 2 ) c(i) t = 4 (2490497145096213450327915910296294089131 t / ----- i = 0 / - 43340630771957380193433293544054431323292 t + 1) / ((t - 1) / 2 (t - 290119316370360939318381049317302688928322 t + 1)) In Maple notation, these generating functions are 8*(11261604924439579270269139914681681294523*t^2+ 93364757732113000857480347698311098764399*t-2)/(t-1)/(t^2-\ 290119316370360939318381049317302688928322*t+1) -(22832394208315801538762109257964240693121*t^2+ 140568140299128865433659401277068308243518*t+1)/(t-1)/(t^2-\ 290119316370360939318381049317302688928322*t+1) 4*(2490497145096213450327915910296294089131*t^2-\ 43340630771957380193433293544054431323292*t+1)/(t-1)/(t^2-\ 290119316370360939318381049317302688928322*t+1) Then for all i>=0 we have 3 3 3 a(i) + 67 b(i) + 67 c(i) = -125 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 47, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- \ i ) a(i) t = 8 ( / ----- i = 0 2 8457704451202097043638914700357 t + 37174777842082794652160480887646 t - 3 / 2 ) / ((t - 1) (t - 72259270930397519221389558374402 t + 1)) / infinity ----- \ i ) b(i) t = - 5 ( / ----- i = 0 2 4297691560190435656545682665161 t + 2100264720105178024514851149238 t + 1) / 2 / ((t - 1) (t - 72259270930397519221389558374402 t + 1)) / infinity ----- \ i ) c(i) t = 7 ( / ----- i = 0 2 2501194512660254239136737049881 t - 7071163284299978297037118345882 t + 1) / 2 / ((t - 1) (t - 72259270930397519221389558374402 t + 1)) / In Maple notation, these generating functions are 8*(8457704451202097043638914700357*t^2+37174777842082794652160480887646*t-3)/(t -1)/(t^2-72259270930397519221389558374402*t+1) -5*(4297691560190435656545682665161*t^2+2100264720105178024514851149238*t+1)/(t -1)/(t^2-72259270930397519221389558374402*t+1) 7*(2501194512660254239136737049881*t^2-7071163284299978297037118345882*t+1)/(t-\ 1)/(t^2-72259270930397519221389558374402*t+1) Then for all i>=0 we have 3 3 3 a(i) + 68 b(i) + 68 c(i) = -1000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 48, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 4036192025215568381 t + 11684367438598436438 t - 19 ) a(i) t = ---------------------------------------------------- / 2 ----- (t - 1) (t - 2713298141975803202 t + 1) i = 0 infinity ----- 2 \ i 2 (537419081451250441 t + 601751894187445558 t + 1) ) b(i) t = - ---------------------------------------------------- / 2 ----- (t - 1) (t - 2713298141975803202 t + 1) i = 0 infinity ----- 2 \ i 5 (134243792076188809 t - 589912182331667210 t + 1) ) c(i) t = ---------------------------------------------------- / 2 ----- (t - 1) (t - 2713298141975803202 t + 1) i = 0 In Maple notation, these generating functions are (4036192025215568381*t^2+11684367438598436438*t-19)/(t-1)/(t^2-\ 2713298141975803202*t+1) -2*(537419081451250441*t^2+601751894187445558*t+1)/(t-1)/(t^2-\ 2713298141975803202*t+1) 5*(134243792076188809*t^2-589912182331667210*t+1)/(t-1)/(t^2-\ 2713298141975803202*t+1) Then for all i>=0 we have 3 3 3 a(i) + 70 b(i) + 70 c(i) = -1331 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 49, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 5 (9953275 t + 11808778 t - 5) ) a(i) t = ------------------------------- / 2 ----- (t - 1) (t - 9424898 t + 1) i = 0 infinity ----- 2 \ i 17614791 t - 10831822 t + 7 ) b(i) t = - ---------------------------- / 2 ----- (t - 1) (t - 9424898 t + 1) i = 0 infinity ----- 2 \ i 15541193 t - 22324178 t + 9 ) c(i) t = ---------------------------- / 2 ----- (t - 1) (t - 9424898 t + 1) i = 0 In Maple notation, these generating functions are 5*(9953275*t^2+11808778*t-5)/(t-1)/(t^2-9424898*t+1) -(17614791*t^2-10831822*t+7)/(t-1)/(t^2-9424898*t+1) (15541193*t^2-22324178*t+9)/(t-1)/(t^2-9424898*t+1) Then for all i>=0 we have 3 3 3 a(i) + 72 b(i) + 72 c(i) = -12167 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 50, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 8 (704941730562773106565 t + 1865297382878977859422 t - 3) ) a(i) t = ----------------------------------------------------------- / 2 ----- (t - 1) (t - 2913139963286990469122 t + 1) i = 0 infinity ----- 2 \ i 1774145575090940903197 t - 159780512102733684898 t + 5 ) b(i) t = - ------------------------------------------------------- / 2 ----- (t - 1) (t - 2913139963286990469122 t + 1) i = 0 infinity ----- 2 \ i 7 (211046857761095430889 t - 441670438187982176362 t + 1) ) c(i) t = ---------------------------------------------------------- / 2 ----- (t - 1) (t - 2913139963286990469122 t + 1) i = 0 In Maple notation, these generating functions are 8*(704941730562773106565*t^2+1865297382878977859422*t-3)/(t-1)/(t^2-\ 2913139963286990469122*t+1) -(1774145575090940903197*t^2-159780512102733684898*t+5)/(t-1)/(t^2-\ 2913139963286990469122*t+1) 7*(211046857761095430889*t^2-441670438187982176362*t+1)/(t-1)/(t^2-\ 2913139963286990469122*t+1) Then for all i>=0 we have 3 3 3 a(i) + 76 b(i) + 76 c(i) = -2744 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 51, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- \ i 2 ) a(i) t = (28869708517780821870815097184416355183 t / ----- i = 0 / + 35357884874193786289260785374006684834 t - 17) / ((t - 1) / 2 (t - 7689900112442742995069326300293120002 t + 1)) infinity ----- \ i 2 ) b(i) t = - 2 (3783211703293084775398849789112860801 t / ----- i = 0 / + 472833641958244680991720741866979198 t + 1) / ((t - 1) / 2 (t - 7689900112442742995069326300293120002 t + 1)) infinity ----- \ i 2 ) c(i) t = 5 (988380890084855330690174512292119681 t / ----- i = 0 / - 2690799028185387113246402724684055682 t + 1) / ((t - 1) / 2 (t - 7689900112442742995069326300293120002 t + 1)) In Maple notation, these generating functions are (28869708517780821870815097184416355183*t^2+ 35357884874193786289260785374006684834*t-17)/(t-1)/(t^2-\ 7689900112442742995069326300293120002*t+1) -2*(3783211703293084775398849789112860801*t^2+ 472833641958244680991720741866979198*t+1)/(t-1)/(t^2-\ 7689900112442742995069326300293120002*t+1) 5*(988380890084855330690174512292119681*t^2-\ 2690799028185387113246402724684055682*t+1)/(t-1)/(t^2-\ 7689900112442742995069326300293120002*t+1) Then for all i>=0 we have 3 3 3 a(i) + 77 b(i) + 77 c(i) = -4096 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 52, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 46426306140291468719764229011 t + 63007561617378524060603903818 t - 29 ----------------------------------------------------------------------- 2 (t - 1) (t - 8667475473908456249850312002 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 6 (2357402558263776563000524841 t - 847584249905529345284664042 t + 1) - ----------------------------------------------------------------------- 2 (t - 1) (t - 8667475473908456249850312002 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 3 (3855058706522155557116526923 t - 6874695323238649992548248526 t + 3) ------------------------------------------------------------------------ 2 (t - 1) (t - 8667475473908456249850312002 t + 1) In Maple notation, these generating functions are (46426306140291468719764229011*t^2+63007561617378524060603903818*t-29)/(t-1)/(t ^2-8667475473908456249850312002*t+1) -6*(2357402558263776563000524841*t^2-847584249905529345284664042*t+1)/(t-1)/(t^ 2-8667475473908456249850312002*t+1) 3*(3855058706522155557116526923*t^2-6874695323238649992548248526*t+3)/(t-1)/(t^ 2-8667475473908456249850312002*t+1) Then for all i>=0 we have 3 3 3 a(i) + 78 b(i) + 78 c(i) = -15625 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 53, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 2 (7787024679593 t + 32720337766814 t - 7) ) a(i) t = ------------------------------------------- / 2 ----- (t - 1) (t - 26803379131202 t + 1) i = 0 infinity ----- 2 \ i 3 (1626522903721 t + 388768760278 t + 1) ) b(i) t = - ----------------------------------------- / 2 ----- (t - 1) (t - 26803379131202 t + 1) i = 0 infinity ----- 2 \ i 4 (1025216560801 t - 2536685308802 t + 1) ) c(i) t = ------------------------------------------ / 2 ----- (t - 1) (t - 26803379131202 t + 1) i = 0 In Maple notation, these generating functions are 2*(7787024679593*t^2+32720337766814*t-7)/(t-1)/(t^2-26803379131202*t+1) -3*(1626522903721*t^2+388768760278*t+1)/(t-1)/(t^2-26803379131202*t+1) 4*(1025216560801*t^2-2536685308802*t+1)/(t-1)/(t^2-26803379131202*t+1) Then for all i>=0 we have 3 3 3 a(i) + 80 b(i) + 80 c(i) = -216 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 54, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 2 (55391 t + 3731534 t - 13) ) a(i) t = ----------------------------- / 2 ----- (t - 1) (t - 15100994 t + 1) i = 0 infinity ----- 2 \ i 8 (4870 t + 47617 t + 1) ) b(i) t = - ----------------------------- / 2 ----- (t - 1) (t - 15100994 t + 1) i = 0 infinity ----- 2 \ i 9 (3873 t - 50530 t + 1) ) c(i) t = ----------------------------- / 2 ----- (t - 1) (t - 15100994 t + 1) i = 0 In Maple notation, these generating functions are 2*(55391*t^2+3731534*t-13)/(t-1)/(t^2-15100994*t+1) -8*(4870*t^2+47617*t+1)/(t-1)/(t^2-15100994*t+1) 9*(3873*t^2-50530*t+1)/(t-1)/(t^2-15100994*t+1) Then for all i>=0 we have 3 3 3 a(i) + 81 b(i) + 81 c(i) = -1 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 55, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 30 (181813661104141247 t + 1159963013101369154 t - 1) ) a(i) t = ------------------------------------------------------ / 2 ----- (t - 1) (t - 5611066092132134402 t + 1) i = 0 infinity ----- 2 \ i 1270400877400583761 t + 6414320074867339438 t + 1 ) b(i) t = - -------------------------------------------------- / 2 ----- (t - 1) (t - 5611066092132134402 t + 1) i = 0 infinity ----- 2 \ i 491199472668549847 t - 8175920424936473054 t + 7 ) c(i) t = ------------------------------------------------- / 2 ----- (t - 1) (t - 5611066092132134402 t + 1) i = 0 In Maple notation, these generating functions are 30*(181813661104141247*t^2+1159963013101369154*t-1)/(t-1)/(t^2-\ 5611066092132134402*t+1) -(1270400877400583761*t^2+6414320074867339438*t+1)/(t-1)/(t^2-\ 5611066092132134402*t+1) (491199472668549847*t^2-8175920424936473054*t+7)/(t-1)/(t^2-5611066092132134402 *t+1) Then for all i>=0 we have 3 3 3 a(i) + 84 b(i) + 84 c(i) = -1728 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 56, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 4 (5440859 t + 134070954 t - 5) ) a(i) t = -------------------------------- / 2 ----- (t - 1) (t - 554602498 t + 1) i = 0 infinity ----- 2 \ i 6770693 t + 31121398 t + 5 ) b(i) t = - ------------------------------ / 2 ----- (t - 1) (t - 554602498 t + 1) i = 0 infinity ----- 2 \ i 2 (2890723 t - 21836774 t + 3) ) c(i) t = ------------------------------- / 2 ----- (t - 1) (t - 554602498 t + 1) i = 0 In Maple notation, these generating functions are 4*(5440859*t^2+134070954*t-5)/(t-1)/(t^2-554602498*t+1) -(6770693*t^2+31121398*t+5)/(t-1)/(t^2-554602498*t+1) 2*(2890723*t^2-21836774*t+3)/(t-1)/(t^2-554602498*t+1) Then for all i>=0 we have 3 3 3 a(i) + 88 b(i) + 88 c(i) = -8 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 57, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 151171 t + 11388058 t - 29 ) a(i) t = ----------------------------- / 2 ----- (t - 1) (t - 23020802 t + 1) i = 0 infinity ----- 2 \ i 52889 t + 523102 t + 9 ) b(i) t = - ----------------------------- / 2 ----- (t - 1) (t - 23020802 t + 1) i = 0 infinity ----- 2 \ i 10 (4785 t - 62386 t + 1) ) c(i) t = ----------------------------- / 2 ----- (t - 1) (t - 23020802 t + 1) i = 0 In Maple notation, these generating functions are (151171*t^2+11388058*t-29)/(t-1)/(t^2-23020802*t+1) -(52889*t^2+523102*t+9)/(t-1)/(t^2-23020802*t+1) 10*(4785*t^2-62386*t+1)/(t-1)/(t^2-23020802*t+1) Then for all i>=0 we have 3 3 3 a(i) + 90 b(i) + 90 c(i) = -1 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 58, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- \ i 2 ) a(i) t = (87708788801677232472178399667448431989534327957933219 t / ----- i = 0 / + 518347122688796309890678735645527950934167885346591610 t - 29) / ( / 2 (t - 1) (t - 117522146315109217345145340151994550775639646579920898 t + 1) ) infinity ----- \ i 2 ) b(i) t = - 4 (5603422057158289318276009729934204146818788204579809 t / ----- i = 0 / + 11524245006702919487630822354997737109720622171417630 t + 1) / ( / 2 (t - 1) (t - 117522146315109217345145340151994550775639646579920898 t + 1) ) infinity ----- \ i 2 ) c(i) t = (15666858320811831698321085099163860280387896821555143 t / ----- i = 0 / - 84177526576256666921948413438891625306545538325544910 t + 7) / ( / 2 (t - 1) (t - 117522146315109217345145340151994550775639646579920898 t + 1) ) In Maple notation, these generating functions are (87708788801677232472178399667448431989534327957933219*t^2+ 518347122688796309890678735645527950934167885346591610*t-29)/(t-1)/(t^2-\ 117522146315109217345145340151994550775639646579920898*t+1) -4*(5603422057158289318276009729934204146818788204579809*t^2+ 11524245006702919487630822354997737109720622171417630*t+1)/(t-1)/(t^2-\ 117522146315109217345145340151994550775639646579920898*t+1) (15666858320811831698321085099163860280387896821555143*t^2-\ 84177526576256666921948413438891625306545538325544910*t+7)/(t-1)/(t^2-\ 117522146315109217345145340151994550775639646579920898*t+1) Then for all i>=0 we have 3 3 3 a(i) + 91 b(i) + 91 c(i) = -1000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 59, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- \ i ) a(i) t = 2 ( / ----- i = 0 2 83259860917721205401422603415441972566825887566385297565571432024283167 t + 6588911551899029508176882790379443571202872188863003764078920903742732046 t / 2 - 13) / ((t - 1) (t - / 24288252609131769522155455998301691669970158181508917241808384092676059202 t + 1)) infinity ----- \ i ) b(i) t = - 3 ( / ----- i = 0 2 12892710293276533439322908199657800151624206524149026573761378138145921 t + 684007205165339595251641291539072991654108281149326813520634339717596478 t / 2 + 1) / ((t - 1) (t - / 24288252609131769522155455998301691669970158181508917241808384092676059202 t + 1)) infinity ----- \ i ) c(i) t = 6 ( / ----- i = 0 2 3362656594130073927016172491849567758522255574430613377044710105210621 t - 351812614323438138272498272361214963661388499411168533424242569033081822 t / 2 + 1) / ((t - 1) (t - / 24288252609131769522155455998301691669970158181508917241808384092676059202 t + 1)) In Maple notation, these generating functions are 2*(83259860917721205401422603415441972566825887566385297565571432024283167*t^2+ 6588911551899029508176882790379443571202872188863003764078920903742732046*t-13) /(t-1)/(t^2-\ 24288252609131769522155455998301691669970158181508917241808384092676059202*t+1) -3*(12892710293276533439322908199657800151624206524149026573761378138145921*t^2 +684007205165339595251641291539072991654108281149326813520634339717596478*t+1)/ (t-1)/(t^2-\ 24288252609131769522155455998301691669970158181508917241808384092676059202*t+1) 6*(3362656594130073927016172491849567758522255574430613377044710105210621*t^2-\ 351812614323438138272498272361214963661388499411168533424242569033081822*t+1)/( t-1)/(t^2-\ 24288252609131769522155455998301691669970158181508917241808384092676059202*t+1) Then for all i>=0 we have 3 3 3 a(i) + 93 b(i) + 93 c(i) = -1 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 60, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- \ i 2 ) a(i) t = 30 (12747083702603642562210108197087642111 t / ----- i = 0 / + 40867884523379905731937356153370092290 t - 1) / ((t - 1) / 2 (t - 155738717227856973616333110732281990402 t + 1)) infinity ----- \ i 2 ) b(i) t = - (86124473415516264445783098599729207761 t / ----- i = 0 / + 189609648889541983924118146631196283438 t + 1) / ((t - 1) / 2 (t - 155738717227856973616333110732281990402 t + 1)) infinity ----- \ i 2 ) c(i) t = (38322909530752604837495192860650549847 t / ----- i = 0 / - 314057031835810853207396438091576041054 t + 7) / ((t - 1) / 2 (t - 155738717227856973616333110732281990402 t + 1)) In Maple notation, these generating functions are 30*(12747083702603642562210108197087642111*t^2+ 40867884523379905731937356153370092290*t-1)/(t-1)/(t^2-\ 155738717227856973616333110732281990402*t+1) -(86124473415516264445783098599729207761*t^2+ 189609648889541983924118146631196283438*t+1)/(t-1)/(t^2-\ 155738717227856973616333110732281990402*t+1) (38322909530752604837495192860650549847*t^2-\ 314057031835810853207396438091576041054*t+7)/(t-1)/(t^2-\ 155738717227856973616333110732281990402*t+1) Then for all i>=0 we have 3 3 3 a(i) + 96 b(i) + 96 c(i) = -5832 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 61, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 21 (232218228479 t + 1425174784322 t - 1) ) a(i) t = ------------------------------------------ / 2 ----- (t - 1) (t - 9682664443202 t + 1) i = 0 infinity ----- 2 \ i 3 (411186641881 t + 810050314918 t + 1) ) b(i) t = - ---------------------------------------- / 2 ----- (t - 1) (t - 9682664443202 t + 1) i = 0 infinity ----- 2 \ i 5 (177046516585 t - 909788690666 t + 1) ) c(i) t = ---------------------------------------- / 2 ----- (t - 1) (t - 9682664443202 t + 1) i = 0 In Maple notation, these generating functions are 21*(232218228479*t^2+1425174784322*t-1)/(t-1)/(t^2-9682664443202*t+1) -3*(411186641881*t^2+810050314918*t+1)/(t-1)/(t^2-9682664443202*t+1) 5*(177046516585*t^2-909788690666*t+1)/(t-1)/(t^2-9682664443202*t+1) Then for all i>=0 we have 3 3 3 a(i) + 98 b(i) + 98 c(i) = -343 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 62, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 126785719 t + 143448922 t - 17 ) a(i) t = ------------------------------- / 2 ----- (t - 1) (t - 33709634 t + 1) i = 0 infinity ----- 2 \ i 44168349 t - 31901858 t + 5 ) b(i) t = - ----------------------------- / 2 ----- (t - 1) (t - 33709634 t + 1) i = 0 infinity ----- 2 \ i 2 (20163179 t - 26296430 t + 3) ) c(i) t = -------------------------------- / 2 ----- (t - 1) (t - 33709634 t + 1) i = 0 In Maple notation, these generating functions are (126785719*t^2+143448922*t-17)/(t-1)/(t^2-33709634*t+1) -(44168349*t^2-31901858*t+5)/(t-1)/(t^2-33709634*t+1) 2*(20163179*t^2-26296430*t+3)/(t-1)/(t^2-33709634*t+1) Then for all i>=0 we have 3 3 3 a(i) + 99 b(i) + 99 c(i) = -4096 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 63, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- \ i 2 ) a(i) t = 6 (50379673390162941378166977868467612027907 t / ----- i = 0 / + 341335286640063113615269677158794065218962 t - 5) / ((t - 1) / 2 (t - 520152895933615351584566513015471096916098 t + 1)) infinity ----- \ i 2 ) b(i) t = - (386297025515862810843723576384652130014769 t / ----- i = 0 / + 154600345529052150250254773407871711194898 t + 29) / ((t - 1) / 2 (t - 520152895933615351584566513015471096916098 t + 1)) infinity ----- \ i 2 ) c(i) t = (339792711617250864956184827582989718912087 t / ----- i = 0 / - 880690082662165826050163177375513560121818 t + 35) / ((t - 1) / 2 (t - 520152895933615351584566513015471096916098 t + 1)) In Maple notation, these generating functions are 6*(50379673390162941378166977868467612027907*t^2+ 341335286640063113615269677158794065218962*t-5)/(t-1)/(t^2-\ 520152895933615351584566513015471096916098*t+1) -(386297025515862810843723576384652130014769*t^2+ 154600345529052150250254773407871711194898*t+29)/(t-1)/(t^2-\ 520152895933615351584566513015471096916098*t+1) (339792711617250864956184827582989718912087*t^2-\ 880690082662165826050163177375513560121818*t+35)/(t-1)/(t^2-\ 520152895933615351584566513015471096916098*t+1) Then for all i>=0 we have 3 3 3 2 a(i) + 3 b(i) + 3 c(i) = -1458 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 64, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 9447985074179029657614217 t + 20627684844450539205266062 t - 23 ---------------------------------------------------------------- 2 (t - 1) (t - 3145168096065837266706434 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 3 (2411394822145609471857841 t + 3158173681304310687934798 t + 1) - ------------------------------------------------------------------ 2 (t - 1) (t - 3145168096065837266706434 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 3454990436765216552527843 t - 20163695947114977031905782 t + 19 ---------------------------------------------------------------- 2 (t - 1) (t - 3145168096065837266706434 t + 1) In Maple notation, these generating functions are (9447985074179029657614217*t^2+20627684844450539205266062*t-23)/(t-1)/(t^2-\ 3145168096065837266706434*t+1) -3*(2411394822145609471857841*t^2+3158173681304310687934798*t+1)/(t-1)/(t^2-\ 3145168096065837266706434*t+1) (3454990436765216552527843*t^2-20163695947114977031905782*t+19)/(t-1)/(t^2-\ 3145168096065837266706434*t+1) Then for all i>=0 we have 3 3 3 2 a(i) + 5 b(i) + 5 c(i) = -9826 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 65, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 74850826223064995714491 t + 426235793388942968608018 t - 29 ) a(i) t = ------------------------------------------------------------ / 2 ----- (t - 1) (t - 99265463315268877599842 t + 1) i = 0 infinity ----- \ i ) b(i) t = / ----- i = 0 2 64556175891288089613797 t + 50346997398303967333946 t + 17 - ----------------------------------------------------------- 2 (t - 1) (t - 99265463315268877599842 t + 1) infinity ----- 2 \ i 53040664164662705657723 t - 167943837454254762605506 t + 23 ) c(i) t = ------------------------------------------------------------ / 2 ----- (t - 1) (t - 99265463315268877599842 t + 1) i = 0 In Maple notation, these generating functions are (74850826223064995714491*t^2+426235793388942968608018*t-29)/(t-1)/(t^2-\ 99265463315268877599842*t+1) -(64556175891288089613797*t^2+50346997398303967333946*t+17)/(t-1)/(t^2-\ 99265463315268877599842*t+1) (53040664164662705657723*t^2-167943837454254762605506*t+23)/(t-1)/(t^2-\ 99265463315268877599842*t+1) Then for all i>=0 we have 3 3 3 2 a(i) + 7 b(i) + 7 c(i) = -2000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 66, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- \ i 2 ) a(i) t = 22 (1760927298297749485285010346930137310780641 t / ----- i = 0 / + 2864753152530352892274430489535322968480228 t - 1) / ((t - 1) / 2 (t - 11966901647220461678581877971659111379934882 t + 1)) infinity ----- \ i 2 ) b(i) t = - (47549978255073857989371016970025107141534473 t / ----- i = 0 / - 39724278308382419506237693279757286126082392 t + 23) / ((t - 1) / 2 (t - 11966901647220461678581877971659111379934882 t + 1)) infinity ----- \ i 2 ) c(i) t = (45563291046737935493152030937591106072961443 t / ----- i = 0 / - 53388990993429373976285354627858927088413572 t + 25) / ((t - 1) / 2 (t - 11966901647220461678581877971659111379934882 t + 1)) In Maple notation, these generating functions are 22*(1760927298297749485285010346930137310780641*t^2+ 2864753152530352892274430489535322968480228*t-1)/(t-1)/(t^2-\ 11966901647220461678581877971659111379934882*t+1) -(47549978255073857989371016970025107141534473*t^2-\ 39724278308382419506237693279757286126082392*t+23)/(t-1)/(t^2-\ 11966901647220461678581877971659111379934882*t+1) (45563291046737935493152030937591106072961443*t^2-\ 53388990993429373976285354627858927088413572*t+25)/(t-1)/(t^2-\ 11966901647220461678581877971659111379934882*t+1) Then for all i>=0 we have 3 3 3 2 a(i) + 9 b(i) + 9 c(i) = -9826 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 67, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 29 (664027824650231569439 t + 2089094283818714326562 t - 1) ) a(i) t = ------------------------------------------------------------ / 2 ----- (t - 1) (t - 10641282555992364129602 t + 1) i = 0 infinity ----- \ i ) b(i) t = / ----- i = 0 2 4 (5668016071537089913927 t - 4307449142642289385934 t + 7) - ------------------------------------------------------------ 2 (t - 1) (t - 10641282555992364129602 t + 1) infinity ----- 2 \ i 30 (726558496030919995321 t - 907967419883560065722 t + 1) ) c(i) t = ----------------------------------------------------------- / 2 ----- (t - 1) (t - 10641282555992364129602 t + 1) i = 0 In Maple notation, these generating functions are 29*(664027824650231569439*t^2+2089094283818714326562*t-1)/(t-1)/(t^2-\ 10641282555992364129602*t+1) -4*(5668016071537089913927*t^2-4307449142642289385934*t+7)/(t-1)/(t^2-\ 10641282555992364129602*t+1) 30*(726558496030919995321*t^2-907967419883560065722*t+1)/(t-1)/(t^2-\ 10641282555992364129602*t+1) Then for all i>=0 we have 3 3 3 2 a(i) + 11 b(i) + 11 c(i) = -6750 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 68, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 4 (193433 t + 935174 t - 7) ) a(i) t = ---------------------------- / 2 ----- (t - 1) (t - 806402 t + 1) i = 0 infinity ----- 2 \ i 11 (45901 t + 47698 t + 1) ) b(i) t = - --------------------------- / 2 ----- (t - 1) (t - 806402 t + 1) i = 0 infinity ----- 2 \ i 385877 t - 1415494 t + 17 ) c(i) t = --------------------------- / 2 ----- (t - 1) (t - 806402 t + 1) i = 0 In Maple notation, these generating functions are 4*(193433*t^2+935174*t-7)/(t-1)/(t^2-806402*t+1) -11*(45901*t^2+47698*t+1)/(t-1)/(t^2-806402*t+1) (385877*t^2-1415494*t+17)/(t-1)/(t^2-806402*t+1) Then for all i>=0 we have 3 3 3 2 a(i) + 13 b(i) + 13 c(i) = -2662 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 69, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 4 (126827124248 t + 317571325553 t - 7) ) a(i) t = ---------------------------------------- / 2 ----- (t - 1) (t - 206364867074 t + 1) i = 0 infinity ----- 2 \ i 326063661857 t + 26322774092 t + 11 ) b(i) t = - ------------------------------------ / 2 ----- (t - 1) (t - 206364867074 t + 1) i = 0 infinity ----- 2 \ i 17 (15201325231 t - 35929939112 t + 1) ) c(i) t = --------------------------------------- / 2 ----- (t - 1) (t - 206364867074 t + 1) i = 0 In Maple notation, these generating functions are 4*(126827124248*t^2+317571325553*t-7)/(t-1)/(t^2-206364867074*t+1) -(326063661857*t^2+26322774092*t+11)/(t-1)/(t^2-206364867074*t+1) 17*(15201325231*t^2-35929939112*t+1)/(t-1)/(t^2-206364867074*t+1) Then for all i>=0 we have 3 3 3 2 a(i) + 15 b(i) + 15 c(i) = -9826 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 70, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 4 (10791512 t + 47432741 t - 3) ) a(i) t = -------------------------------- / 2 ----- (t - 1) (t - 92198402 t + 1) i = 0 infinity ----- 2 \ i 5 (5483591 t + 2679808 t + 1) ) b(i) t = - ------------------------------ / 2 ----- (t - 1) (t - 92198402 t + 1) i = 0 infinity ----- 2 \ i 7 (3191371 t - 9022372 t + 1) ) c(i) t = ------------------------------ / 2 ----- (t - 1) (t - 92198402 t + 1) i = 0 In Maple notation, these generating functions are 4*(10791512*t^2+47432741*t-3)/(t-1)/(t^2-92198402*t+1) -5*(5483591*t^2+2679808*t+1)/(t-1)/(t^2-92198402*t+1) 7*(3191371*t^2-9022372*t+1)/(t-1)/(t^2-92198402*t+1) Then for all i>=0 we have 3 3 3 2 a(i) + 17 b(i) + 17 c(i) = -250 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 71, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- \ i ) a(i) t = ( / ----- i = 0 2 2050526009193022886180926778209655165682642804771620163733 t + 192665777303746091114102038382299798019390065054241150437894 t - 27) / / ((t - 1) / 2 (t - 331171035555864949795756854131260172346265392894068964172802 t + 1)) infinity ----- \ i ) b(i) t = - 5 ( / ----- i = 0 2 198265842740466428723937503232266142529768649682698446537 t / + 14827086696368221108305771619389723158365605657548208261302 t + 1) / ( / (t - 1) 2 (t - 331171035555864949795756854131260172346265392894068964172802 t + 1)) infinity ----- \ i ) c(i) t = ( / ----- i = 0 2 405464639647182747567994150958572093882373875621600757333 t / - 75532227335190620432716539764068518598359245411776134296546 t + 13) / / ((t - 1) 2 (t - 331171035555864949795756854131260172346265392894068964172802 t + 1)) In Maple notation, these generating functions are (2050526009193022886180926778209655165682642804771620163733*t^2+ 192665777303746091114102038382299798019390065054241150437894*t-27)/(t-1)/(t^2-\ 331171035555864949795756854131260172346265392894068964172802*t+1) -5*(198265842740466428723937503232266142529768649682698446537*t^2+ 14827086696368221108305771619389723158365605657548208261302*t+1)/(t-1)/(t^2-\ 331171035555864949795756854131260172346265392894068964172802*t+1) (405464639647182747567994150958572093882373875621600757333*t^2-\ 75532227335190620432716539764068518598359245411776134296546*t+13)/(t-1)/(t^2-\ 331171035555864949795756854131260172346265392894068964172802*t+1) Then for all i>=0 we have 3 3 3 2 a(i) + 19 b(i) + 19 c(i) = -2 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 72, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 9 (479196533 t + 1880989870 t - 3) ) a(i) t = ----------------------------------- / 2 ----- (t - 1) (t - 2368768898 t + 1) i = 0 infinity ----- 2 \ i 2008996549 t + 6101462170 t + 1 ) b(i) t = - -------------------------------- / 2 ----- (t - 1) (t - 2368768898 t + 1) i = 0 infinity ----- 2 \ i 13 (59752069 t - 683633510 t + 1) ) c(i) t = ---------------------------------- / 2 ----- (t - 1) (t - 2368768898 t + 1) i = 0 In Maple notation, these generating functions are 9*(479196533*t^2+1880989870*t-3)/(t-1)/(t^2-2368768898*t+1) -(2008996549*t^2+6101462170*t+1)/(t-1)/(t^2-2368768898*t+1) 13*(59752069*t^2-683633510*t+1)/(t-1)/(t^2-2368768898*t+1) Then for all i>=0 we have 3 3 3 2 a(i) + 21 b(i) + 21 c(i) = -6750 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 73, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 4369204181 t + 46098310238 t - 19 ) a(i) t = ---------------------------------- / 2 ----- (t - 1) (t - 25091193602 t + 1) i = 0 infinity ----- 2 \ i 9 (301126801 t + 427531598 t + 1) ) b(i) t = - ---------------------------------- / 2 ----- (t - 1) (t - 25091193602 t + 1) i = 0 infinity ----- 2 \ i 2330210411 t - 8888136022 t + 11 ) c(i) t = --------------------------------- / 2 ----- (t - 1) (t - 25091193602 t + 1) i = 0 In Maple notation, these generating functions are (4369204181*t^2+46098310238*t-19)/(t-1)/(t^2-25091193602*t+1) -9*(301126801*t^2+427531598*t+1)/(t-1)/(t^2-25091193602*t+1) (2330210411*t^2-8888136022*t+11)/(t-1)/(t^2-25091193602*t+1) Then for all i>=0 we have 3 3 3 2 a(i) + 23 b(i) + 23 c(i) = -128 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 74, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- \ i ) a(i) t = 30 (56272750355689801843762317482843615434785150801999403\ / ----- i = 0 2 04141886173263752817649 t + 1161131017077271977660247118682216182324601\ / 2 58224258066376429110640458571724852 t - 1) / ((t - 1) (t - 1182089765\ / 018875865289389315115996994465602995750157133570124488145456464260002 t + 1 )) infinity ----- \ i ) b(i) t = - 3 (2459220504162073931268373838711290264491663068507128\ / ----- i = 0 2 7258813851528753430843551 t + 43077256292948710187583887514027587666966\ / 2 3139690382325515841022049291905231448 t + 1) / ((t - 1) (t - 11820897\ / 65018875865289389315115996994465602995750157133570124488145456464260002 t + 1)) infinity ----- \ i ) c(i) t = (25542829105699530643397800176044180419219762796357230598\ / ----- i = 0 2 082530243999554093663 t - 139163713301902305420896564075821051836295907\ / 2 3922718068922047150978135562318676 t + 13) / ((t - 1) (t - 1182089765\ / 018875865289389315115996994465602995750157133570124488145456464260002 t + 1 )) In Maple notation, these generating functions are 30*( 5627275035568980184376231748284361543478515080199940304141886173263752817649*t^ 2+ 116113101707727197766024711868221618232460158224258066376429110640458571724852* t-1)/(t-1)/(t^2-118208976501887586528938931511599699446560299575015713357012448\ 8145456464260002*t+1) -3*( 24592205041620739312683738387112902644916630685071287258813851528753430843551*t ^2+ 430772562929487101875838875140275876669663139690382325515841022049291905231448* t+1)/(t-1)/(t^2-118208976501887586528938931511599699446560299575015713357012448\ 8145456464260002*t+1) (25542829105699530643397800176044180419219762796357230598082530243999554093663* t^2-139163713301902305420896564075821051836295907392271806892204715097813556231\ 8676*t+13)/(t-1)/(t^2-118208976501887586528938931511599699446560299575015713357\ 0124488145456464260002*t+1) Then for all i>=0 we have 3 3 3 2 a(i) + 25 b(i) + 25 c(i) = -250 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 75, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 20 (2932163174 t + 11407494437 t - 1) ) a(i) t = -------------------------------------- / 2 ----- (t - 1) (t - 63505008002 t + 1) i = 0 infinity ----- 2 \ i 9 (3984416671 t - 695764472 t + 1) ) b(i) t = - ----------------------------------- / 2 ----- (t - 1) (t - 63505008002 t + 1) i = 0 infinity ----- 2 \ i 31815387041 t - 61413256852 t + 11 ) c(i) t = ----------------------------------- / 2 ----- (t - 1) (t - 63505008002 t + 1) i = 0 In Maple notation, these generating functions are 20*(2932163174*t^2+11407494437*t-1)/(t-1)/(t^2-63505008002*t+1) -9*(3984416671*t^2-695764472*t+1)/(t-1)/(t^2-63505008002*t+1) (31815387041*t^2-61413256852*t+11)/(t-1)/(t^2-63505008002*t+1) Then for all i>=0 we have 3 3 3 2 a(i) + 29 b(i) + 29 c(i) = -1458 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 76, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 4 (3825257116 t + 11002125151 t - 5) ) a(i) t = ------------------------------------- / 2 ----- (t - 1) (t - 10749957122 t + 1) i = 0 infinity ----- 2 \ i 9 (1035892999 t - 399480608 t + 1) ) b(i) t = - ----------------------------------- / 2 ----- (t - 1) (t - 10749957122 t + 1) i = 0 infinity ----- 2 \ i 11 (757806715 t - 1278507764 t + 1) ) c(i) t = ------------------------------------ / 2 ----- (t - 1) (t - 10749957122 t + 1) i = 0 In Maple notation, these generating functions are 4*(3825257116*t^2+11002125151*t-5)/(t-1)/(t^2-10749957122*t+1) -9*(1035892999*t^2-399480608*t+1)/(t-1)/(t^2-10749957122*t+1) 11*(757806715*t^2-1278507764*t+1)/(t-1)/(t^2-10749957122*t+1) Then for all i>=0 we have 3 3 3 2 a(i) + 31 b(i) + 31 c(i) = -2662 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 77, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 9 (11135956213 t + 124040899166 t - 3) ) a(i) t = --------------------------------------- / 2 ----- (t - 1) (t - 376792179554 t + 1) i = 0 infinity ----- 2 \ i 42102359057 t + 274019893274 t + 5 ) b(i) t = - ----------------------------------- / 2 ----- (t - 1) (t - 376792179554 t + 1) i = 0 infinity ----- 2 \ i 23879885255 t - 340002137602 t + 11 ) c(i) t = ------------------------------------ / 2 ----- (t - 1) (t - 376792179554 t + 1) i = 0 In Maple notation, these generating functions are 9*(11135956213*t^2+124040899166*t-3)/(t-1)/(t^2-376792179554*t+1) -(42102359057*t^2+274019893274*t+5)/(t-1)/(t^2-376792179554*t+1) (23879885255*t^2-340002137602*t+11)/(t-1)/(t^2-376792179554*t+1) Then for all i>=0 we have 3 3 3 2 a(i) + 33 b(i) + 33 c(i) = -432 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 78, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 4 (479999969 t + 1814714987 t - 6) ) a(i) t = ----------------------------------- / 2 ----- (t - 1) (t - 1664803202 t + 1) i = 0 infinity ----- 2 \ i 11 (105719731 t - 34312732 t + 1) ) b(i) t = - ---------------------------------- / 2 ----- (t - 1) (t - 1664803202 t + 1) i = 0 infinity ----- 2 \ i 1053202763 t - 1838679776 t + 13 ) c(i) t = --------------------------------- / 2 ----- (t - 1) (t - 1664803202 t + 1) i = 0 In Maple notation, these generating functions are 4*(479999969*t^2+1814714987*t-6)/(t-1)/(t^2-1664803202*t+1) -11*(105719731*t^2-34312732*t+1)/(t-1)/(t^2-1664803202*t+1) (1053202763*t^2-1838679776*t+13)/(t-1)/(t^2-1664803202*t+1) Then for all i>=0 we have 3 3 3 2 a(i) + 35 b(i) + 35 c(i) = -2662 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 79, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 12872660897174834906611 t + 261129855853367943827818 t - 29 ) a(i) t = ------------------------------------------------------------ / 2 ----- (t - 1) (t - 67022198341859384726402 t + 1) i = 0 infinity ----- 2 \ i 4892251802505432886441 t + 91698563454880150983958 t + 1 ) b(i) t = - --------------------------------------------------------- / 2 ----- (t - 1) (t - 67022198341859384726402 t + 1) i = 0 infinity ----- 2 \ i 1214348689026908627411 t - 97805163946412492497822 t + 11 ) c(i) t = ---------------------------------------------------------- / 2 ----- (t - 1) (t - 67022198341859384726402 t + 1) i = 0 In Maple notation, these generating functions are (12872660897174834906611*t^2+261129855853367943827818*t-29)/(t-1)/(t^2-\ 67022198341859384726402*t+1) -(4892251802505432886441*t^2+91698563454880150983958*t+1)/(t-1)/(t^2-\ 67022198341859384726402*t+1) (1214348689026908627411*t^2-97805163946412492497822*t+11)/(t-1)/(t^2-\ 67022198341859384726402*t+1) Then for all i>=0 we have 3 3 3 2 a(i) + 37 b(i) + 37 c(i) = -432 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 80, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 4 (140627492 t + 521124749 t - 7) ) a(i) t = ---------------------------------- / 2 ----- (t - 1) (t - 406506242 t + 1) i = 0 infinity ----- 2 \ i 13 (26029879 t - 11148848 t + 1) ) b(i) t = - --------------------------------- / 2 ----- (t - 1) (t - 406506242 t + 1) i = 0 infinity ----- 2 \ i 3 (103649639 t - 168134116 t + 5) ) c(i) t = ---------------------------------- / 2 ----- (t - 1) (t - 406506242 t + 1) i = 0 In Maple notation, these generating functions are 4*(140627492*t^2+521124749*t-7)/(t-1)/(t^2-406506242*t+1) -13*(26029879*t^2-11148848*t+1)/(t-1)/(t^2-406506242*t+1) 3*(103649639*t^2-168134116*t+5)/(t-1)/(t^2-406506242*t+1) Then for all i>=0 we have 3 3 3 2 a(i) + 41 b(i) + 41 c(i) = -4394 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 81, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 4 (854225222 t + 2552373695 t - 7) ) a(i) t = ----------------------------------- / 2 ----- (t - 1) (t - 1813908098 t + 1) i = 0 infinity ----- 2 \ i 13 (157821379 t - 84771260 t + 1) ) b(i) t = - ---------------------------------- / 2 ----- (t - 1) (t - 1813908098 t + 1) i = 0 infinity ----- 2 \ i 15 (126183487 t - 189493592 t + 1) ) c(i) t = ----------------------------------- / 2 ----- (t - 1) (t - 1813908098 t + 1) i = 0 In Maple notation, these generating functions are 4*(854225222*t^2+2552373695*t-7)/(t-1)/(t^2-1813908098*t+1) -13*(157821379*t^2-84771260*t+1)/(t-1)/(t^2-1813908098*t+1) 15*(126183487*t^2-189493592*t+1)/(t-1)/(t^2-1813908098*t+1) Then for all i>=0 we have 3 3 3 2 a(i) + 43 b(i) + 43 c(i) = -6750 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 82, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 19180322983 t + 34155359434 t - 17 ) a(i) t = ----------------------------------- / 2 ----- (t - 1) (t - 7885795202 t + 1) i = 0 infinity ----- 2 \ i 7629363223 t + 2760704774 t + 3 ) b(i) t = - -------------------------------- / 2 ----- (t - 1) (t - 7885795202 t + 1) i = 0 infinity ----- 2 \ i 5071986827 t - 15462054834 t + 7 ) c(i) t = --------------------------------- / 2 ----- (t - 1) (t - 7885795202 t + 1) i = 0 In Maple notation, these generating functions are (19180322983*t^2+34155359434*t-17)/(t-1)/(t^2-7885795202*t+1) -(7629363223*t^2+2760704774*t+3)/(t-1)/(t^2-7885795202*t+1) (5071986827*t^2-15462054834*t+7)/(t-1)/(t^2-7885795202*t+1) Then for all i>=0 we have 3 3 3 2 a(i) + 45 b(i) + 45 c(i) = -4394 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 83, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 3 (6796673831041832911 t + 11932292246410083098 t - 9) ) a(i) t = ------------------------------------------------------- / 2 ----- (t - 1) (t - 5611066092132134402 t + 1) i = 0 infinity ----- 2 \ i 13 (938719211146809121 t - 663092009714733122 t + 1) ) b(i) t = - ----------------------------------------------------- / 2 ----- (t - 1) (t - 5611066092132134402 t + 1) i = 0 infinity ----- 2 \ i 15 (755712617055956561 t - 994589524963755762 t + 1) ) c(i) t = ----------------------------------------------------- / 2 ----- (t - 1) (t - 5611066092132134402 t + 1) i = 0 In Maple notation, these generating functions are 3*(6796673831041832911*t^2+11932292246410083098*t-9)/(t-1)/(t^2-\ 5611066092132134402*t+1) -13*(938719211146809121*t^2-663092009714733122*t+1)/(t-1)/(t^2-\ 5611066092132134402*t+1) 15*(755712617055956561*t^2-994589524963755762*t+1)/(t-1)/(t^2-\ 5611066092132134402*t+1) Then for all i>=0 we have 3 3 3 2 a(i) + 47 b(i) + 47 c(i) = -16000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 84, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 5334196820000028596271089251 t + 14001923344447428659636830906 t - 29 ---------------------------------------------------------------------- 2 (t - 1) (t - 1827890766695339597518122242 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 2 (881939254718976972186067345 t + 1370812609100144261511942766 t + 1) - ----------------------------------------------------------------------- 2 (t - 1) (t - 1827890766695339597518122242 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 2 (437422853052307922496809909 t - 2690174716871429156194820026 t + 5) ----------------------------------------------------------------------- 2 (t - 1) (t - 1827890766695339597518122242 t + 1) In Maple notation, these generating functions are (5334196820000028596271089251*t^2+14001923344447428659636830906*t-29)/(t-1)/(t^ 2-1827890766695339597518122242*t+1) -2*(881939254718976972186067345*t^2+1370812609100144261511942766*t+1)/(t-1)/(t^ 2-1827890766695339597518122242*t+1) 2*(437422853052307922496809909*t^2-2690174716871429156194820026*t+5)/(t-1)/(t^2 -1827890766695339597518122242*t+1) Then for all i>=0 we have 3 3 3 2 a(i) + 63 b(i) + 63 c(i) = -13718 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 85, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 14369949827977 t + 17534389782046 t - 23 ) a(i) t = ----------------------------------------- / 2 ----- (t - 1) (t - 2739031620002 t + 1) i = 0 infinity ----- 2 \ i 3 (1634979368301 t + 413088081698 t + 1) ) b(i) t = - ----------------------------------------- / 2 ----- (t - 1) (t - 2739031620002 t + 1) i = 0 infinity ----- 2 \ i 3 (996314931503 t - 3044382381506 t + 3) ) c(i) t = ----------------------------------------- / 2 ----- (t - 1) (t - 2739031620002 t + 1) i = 0 In Maple notation, these generating functions are (14369949827977*t^2+17534389782046*t-23)/(t-1)/(t^2-2739031620002*t+1) -3*(1634979368301*t^2+413088081698*t+1)/(t-1)/(t^2-2739031620002*t+1) 3*(996314931503*t^2-3044382381506*t+3)/(t-1)/(t^2-2739031620002*t+1) Then for all i>=0 we have 3 3 3 2 a(i) + 65 b(i) + 65 c(i) = -21296 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 86, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- \ i 2 ) a(i) t = (8044738214454437415066246135217 t / ----- i = 0 / + 10592487833890690183288914307846 t - 23) / ((t - 1) / 2 (t - 1859018893886989033805871279362 t + 1)) infinity ----- \ i ) b(i) t = - 9 / ----- i = 0 2 (434046646353299725502823940561 t - 289815111660573864328476173042 t + 1) / 2 / ((t - 1) (t - 1859018893886989033805871279362 t + 1)) / infinity ----- \ i ) c(i) t = ( / ----- i = 0 2 3532245946739956254406055179691 t - 4830329758974489004975185087382 t + 11 / 2 ) / ((t - 1) (t - 1859018893886989033805871279362 t + 1)) / In Maple notation, these generating functions are (8044738214454437415066246135217*t^2+10592487833890690183288914307846*t-23)/(t-\ 1)/(t^2-1859018893886989033805871279362*t+1) -9*(434046646353299725502823940561*t^2-289815111660573864328476173042*t+1)/(t-1 )/(t^2-1859018893886989033805871279362*t+1) (3532245946739956254406055179691*t^2-4830329758974489004975185087382*t+11)/(t-1 )/(t^2-1859018893886989033805871279362*t+1) Then for all i>=0 we have 3 3 3 2 a(i) + 67 b(i) + 67 c(i) = -16000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 87, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 1694593 t + 9418630 t - 23 ) a(i) t = ---------------------------- / 2 ----- (t - 1) (t - 1876898 t + 1) i = 0 infinity ----- 2 \ i 512989 t + 2203570 t + 1 ) b(i) t = - ---------------------------- / 2 ----- (t - 1) (t - 1876898 t + 1) i = 0 infinity ----- 2 \ i 7 (29269 t - 417350 t + 1) ) c(i) t = ---------------------------- / 2 ----- (t - 1) (t - 1876898 t + 1) i = 0 In Maple notation, these generating functions are (1694593*t^2+9418630*t-23)/(t-1)/(t^2-1876898*t+1) -(512989*t^2+2203570*t+1)/(t-1)/(t^2-1876898*t+1) 7*(29269*t^2-417350*t+1)/(t-1)/(t^2-1876898*t+1) Then for all i>=0 we have 3 3 3 2 a(i) + 77 b(i) + 77 c(i) = -2000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 88, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 4741026626491 t + 6462269673538 t - 29 ) a(i) t = --------------------------------------- / 2 ----- (t - 1) (t - 885289046402 t + 1) i = 0 infinity ----- 2 \ i 1752680702347 t - 518031722354 t + 7 ) b(i) t = - ------------------------------------- / 2 ----- (t - 1) (t - 885289046402 t + 1) i = 0 infinity ----- 2 \ i 1401493544831 t - 2636142524842 t + 11 ) c(i) t = --------------------------------------- / 2 ----- (t - 1) (t - 885289046402 t + 1) i = 0 In Maple notation, these generating functions are (4741026626491*t^2+6462269673538*t-29)/(t-1)/(t^2-885289046402*t+1) -(1752680702347*t^2-518031722354*t+7)/(t-1)/(t^2-885289046402*t+1) (1401493544831*t^2-2636142524842*t+11)/(t-1)/(t^2-885289046402*t+1) Then for all i>=0 we have 3 3 3 2 a(i) + 81 b(i) + 81 c(i) = -31250 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 89, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 2 (484069939 t + 985877572 t - 11) ) a(i) t = ----------------------------------- / 2 ----- (t - 1) (t - 306180002 t + 1) i = 0 infinity ----- 2 \ i 281316151 t + 345218848 t + 1 ) b(i) t = - ------------------------------ / 2 ----- (t - 1) (t - 306180002 t + 1) i = 0 infinity ----- 2 \ i 132371557 t - 758906564 t + 7 ) c(i) t = ------------------------------ / 2 ----- (t - 1) (t - 306180002 t + 1) i = 0 In Maple notation, these generating functions are 2*(484069939*t^2+985877572*t-11)/(t-1)/(t^2-306180002*t+1) -(281316151*t^2+345218848*t+1)/(t-1)/(t^2-306180002*t+1) (132371557*t^2-758906564*t+7)/(t-1)/(t^2-306180002*t+1) Then for all i>=0 we have 3 3 3 2 a(i) + 91 b(i) + 91 c(i) = -9826 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 90, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 2 (9893 t + 352514 t - 7) ) a(i) t = ---------------------------- / 2 ----- (t - 1) (t - 1435202 t + 1) i = 0 infinity ----- 2 \ i 12 (1811 t + 16188 t + 1) ) b(i) t = - ---------------------------- / 2 ----- (t - 1) (t - 1435202 t + 1) i = 0 infinity ----- 2 \ i 15 (1185 t - 15586 t + 1) ) c(i) t = ---------------------------- / 2 ----- (t - 1) (t - 1435202 t + 1) i = 0 In Maple notation, these generating functions are 2*(9893*t^2+352514*t-7)/(t-1)/(t^2-1435202*t+1) -12*(1811*t^2+16188*t+1)/(t-1)/(t^2-1435202*t+1) 15*(1185*t^2-15586*t+1)/(t-1)/(t^2-1435202*t+1) Then for all i>=0 we have 3 3 3 3 a(i) + 5 b(i) + 5 c(i) = -3 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 91, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- \ i ) a(i) t = 2 / ----- i = 0 2 (1949311402855681465823325251 t + 145990364812460127718295141834 t - 13) / 2 / ((t - 1) (t - 554992631482309011968823124994 t + 1)) / infinity ----- \ i ) b(i) t = / ----- i = 0 2 12 (264524756240471495595187465 t + 11553141686994815036863980022 t + 1) - ------------------------------------------------------------------------- 2 (t - 1) (t - 554992631482309011968823124994 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 3 (624918713216178989975566471 t - 47895584486157325119812236430 t + 7) ------------------------------------------------------------------------ 2 (t - 1) (t - 554992631482309011968823124994 t + 1) In Maple notation, these generating functions are 2*(1949311402855681465823325251*t^2+145990364812460127718295141834*t-13)/(t-1)/ (t^2-554992631482309011968823124994*t+1) -12*(264524756240471495595187465*t^2+11553141686994815036863980022*t+1)/(t-1)/( t^2-554992631482309011968823124994*t+1) 3*(624918713216178989975566471*t^2-47895584486157325119812236430*t+7)/(t-1)/(t^ 2-554992631482309011968823124994*t+1) Then for all i>=0 we have 3 3 3 3 a(i) + 7 b(i) + 7 c(i) = -3 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 92, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 5 (9953275 t + 11808778 t - 5) ) a(i) t = ------------------------------- / 2 ----- (t - 1) (t - 9424898 t + 1) i = 0 infinity ----- 2 \ i 3 (17614791 t - 10831822 t + 7) ) b(i) t = - -------------------------------- / 2 ----- (t - 1) (t - 9424898 t + 1) i = 0 infinity ----- 2 \ i 3 (15541193 t - 22324178 t + 9) ) c(i) t = -------------------------------- / 2 ----- (t - 1) (t - 9424898 t + 1) i = 0 In Maple notation, these generating functions are 5*(9953275*t^2+11808778*t-5)/(t-1)/(t^2-9424898*t+1) -3*(17614791*t^2-10831822*t+7)/(t-1)/(t^2-9424898*t+1) 3*(15541193*t^2-22324178*t+9)/(t-1)/(t^2-9424898*t+1) Then for all i>=0 we have 3 3 3 3 a(i) + 8 b(i) + 8 c(i) = -36501 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 93, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 151171 t + 11388058 t - 29 ) a(i) t = ----------------------------- / 2 ----- (t - 1) (t - 23020802 t + 1) i = 0 infinity ----- 2 \ i 3 (52889 t + 523102 t + 9) ) b(i) t = - ----------------------------- / 2 ----- (t - 1) (t - 23020802 t + 1) i = 0 infinity ----- 2 \ i 30 (4785 t - 62386 t + 1) ) c(i) t = ----------------------------- / 2 ----- (t - 1) (t - 23020802 t + 1) i = 0 In Maple notation, these generating functions are (151171*t^2+11388058*t-29)/(t-1)/(t^2-23020802*t+1) -3*(52889*t^2+523102*t+9)/(t-1)/(t^2-23020802*t+1) 30*(4785*t^2-62386*t+1)/(t-1)/(t^2-23020802*t+1) Then for all i>=0 we have 3 3 3 3 a(i) + 10 b(i) + 10 c(i) = -3 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 94, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 9739 t + 183058 t - 29 ) a(i) t = -------------------------- / 2 ----- (t - 1) (t - 91202 t + 1) i = 0 infinity ----- 2 \ i 6899 t + 69122 t + 11 ) b(i) t = - -------------------------- / 2 ----- (t - 1) (t - 91202 t + 1) i = 0 infinity ----- 2 \ i 4 (1061 t - 20074 t + 5) ) c(i) t = -------------------------- / 2 ----- (t - 1) (t - 91202 t + 1) i = 0 In Maple notation, these generating functions are (9739*t^2+183058*t-29)/(t-1)/(t^2-91202*t+1) -(6899*t^2+69122*t+11)/(t-1)/(t^2-91202*t+1) 4*(1061*t^2-20074*t+5)/(t-1)/(t^2-91202*t+1) Then for all i>=0 we have 3 3 3 3 a(i) + 11 b(i) + 11 c(i) = -192 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 95, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 1645409783 t + 3549471458 t - 25 ) a(i) t = --------------------------------- / 2 ----- (t - 1) (t - 590587202 t + 1) i = 0 infinity ----- 2 \ i 8 (140100409 t + 63937942 t + 1) ) b(i) t = - --------------------------------- / 2 ----- (t - 1) (t - 590587202 t + 1) i = 0 infinity ----- 2 \ i 17 (45189145 t - 141207194 t + 1) ) c(i) t = ---------------------------------- / 2 ----- (t - 1) (t - 590587202 t + 1) i = 0 In Maple notation, these generating functions are (1645409783*t^2+3549471458*t-25)/(t-1)/(t^2-590587202*t+1) -8*(140100409*t^2+63937942*t+1)/(t-1)/(t^2-590587202*t+1) 17*(45189145*t^2-141207194*t+1)/(t-1)/(t^2-590587202*t+1) Then for all i>=0 we have 3 3 3 3 a(i) + 14 b(i) + 14 c(i) = -14739 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 96, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 453851107 t + 981534778 t - 29 ) a(i) t = ------------------------------- / 2 ----- (t - 1) (t - 150945794 t + 1) i = 0 infinity ----- 2 \ i 24 (19498337 t - 13895010 t + 1) ) b(i) t = - --------------------------------- / 2 ----- (t - 1) (t - 150945794 t + 1) i = 0 infinity ----- 2 \ i 3 (146531465 t - 191358098 t + 9) ) c(i) t = ---------------------------------- / 2 ----- (t - 1) (t - 150945794 t + 1) i = 0 In Maple notation, these generating functions are (453851107*t^2+981534778*t-29)/(t-1)/(t^2-150945794*t+1) -24*(19498337*t^2-13895010*t+1)/(t-1)/(t^2-150945794*t+1) 3*(146531465*t^2-191358098*t+9)/(t-1)/(t^2-150945794*t+1) Then for all i>=0 we have 3 3 3 3 a(i) + 16 b(i) + 16 c(i) = -20577 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 97, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 2 (577827743 t + 625568270 t - 13) ) a(i) t = ----------------------------------- / 2 ----- (t - 1) (t - 192376898 t + 1) i = 0 infinity ----- 2 \ i 24 (49561614 t - 40718215 t + 1) ) b(i) t = - --------------------------------- / 2 ----- (t - 1) (t - 192376898 t + 1) i = 0 infinity ----- 2 \ i 3 (373833001 t - 444580210 t + 9) ) c(i) t = ---------------------------------- / 2 ----- (t - 1) (t - 192376898 t + 1) i = 0 In Maple notation, these generating functions are 2*(577827743*t^2+625568270*t-13)/(t-1)/(t^2-192376898*t+1) -24*(49561614*t^2-40718215*t+1)/(t-1)/(t^2-192376898*t+1) 3*(373833001*t^2-444580210*t+9)/(t-1)/(t^2-192376898*t+1) Then for all i>=0 we have 3 3 3 3 a(i) + 17 b(i) + 17 c(i) = -46875 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 98, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 2028233707 t + 2177341234 t - 29 ) a(i) t = --------------------------------- / 2 ----- (t - 1) (t - 300190274 t + 1) i = 0 infinity ----- 2 \ i 3 (693791393 t - 583169450 t + 9) ) b(i) t = - ---------------------------------- / 2 ----- (t - 1) (t - 300190274 t + 1) i = 0 infinity ----- 2 \ i 6 (329104173 t - 384415154 t + 5) ) c(i) t = ---------------------------------- / 2 ----- (t - 1) (t - 300190274 t + 1) i = 0 In Maple notation, these generating functions are (2028233707*t^2+2177341234*t-29)/(t-1)/(t^2-300190274*t+1) -3*(693791393*t^2-583169450*t+9)/(t-1)/(t^2-300190274*t+1) 6*(329104173*t^2-384415154*t+5)/(t-1)/(t^2-300190274*t+1) Then for all i>=0 we have 3 3 3 3 a(i) + 19 b(i) + 19 c(i) = -65856 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 99, : Let a(i), b(i), c(i) be defined in terms of the follow\ ing generating functions infinity ----- 2 \ i 2 (3773106873036849587 t + 60933703661115028826 t - 13) ) a(i) t = -------------------------------------------------------- / 2 ----- (t - 1) (t - 62185765967886220802 t + 1) i = 0 infinity ----- 2 \ i 3 (1500829930441234963 t + 11104392900887053034 t + 3) ) b(i) t = - ------------------------------------------------------- / 2 ----- (t - 1) (t - 62185765967886220802 t + 1) i = 0 infinity ----- 2 \ i 15 (199549802807264337 t - 2720594369072921938 t + 1) ) c(i) t = ------------------------------------------------------ / 2 ----- (t - 1) (t - 62185765967886220802 t + 1) i = 0 In Maple notation, these generating functions are 2*(3773106873036849587*t^2+60933703661115028826*t-13)/(t-1)/(t^2-\ 62185765967886220802*t+1) -3*(1500829930441234963*t^2+11104392900887053034*t+3)/(t-1)/(t^2-\ 62185765967886220802*t+1) 15*(199549802807264337*t^2-2720594369072921938*t+1)/(t-1)/(t^2-\ 62185765967886220802*t+1) Then for all i>=0 we have 3 3 3 3 a(i) + 20 b(i) + 20 c(i) = -192 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 100, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 124765329132835 t + 327500959097146 t - 29 ) a(i) t = ------------------------------------------- / 2 ----- (t - 1) (t - 42753839204162 t + 1) i = 0 infinity ----- 2 \ i 3 (20628305460649 t + 32062912585558 t + 1) ) b(i) t = - -------------------------------------------- / 2 ----- (t - 1) (t - 42753839204162 t + 1) i = 0 infinity ----- 2 \ i 3 (10231194699581 t - 62922412745794 t + 5) ) c(i) t = -------------------------------------------- / 2 ----- (t - 1) (t - 42753839204162 t + 1) i = 0 In Maple notation, these generating functions are (124765329132835*t^2+327500959097146*t-29)/(t-1)/(t^2-42753839204162*t+1) -3*(20628305460649*t^2+32062912585558*t+1)/(t-1)/(t^2-42753839204162*t+1) 3*(10231194699581*t^2-62922412745794*t+5)/(t-1)/(t^2-42753839204162*t+1) Then for all i>=0 we have 3 3 3 3 a(i) + 28 b(i) + 28 c(i) = -20577 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 101, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (1354739 t + 1923098 t - 13) ) a(i) t = ------------------------------- / 2 ----- (t - 1) (t - 586754 t + 1) i = 0 infinity ----- 2 \ i 3 (506851 t - 101350 t + 3) ) b(i) t = - ---------------------------- / 2 ----- (t - 1) (t - 586754 t + 1) i = 0 infinity ----- 2 \ i 3 (393957 t - 799466 t + 5) ) c(i) t = ---------------------------- / 2 ----- (t - 1) (t - 586754 t + 1) i = 0 In Maple notation, these generating functions are 2*(1354739*t^2+1923098*t-13)/(t-1)/(t^2-586754*t+1) -3*(506851*t^2-101350*t+3)/(t-1)/(t^2-586754*t+1) 3*(393957*t^2-799466*t+5)/(t-1)/(t^2-586754*t+1) Then for all i>=0 we have 3 3 3 3 a(i) + 32 b(i) + 32 c(i) = -31944 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 102, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2714094099341 t + 8105149294406 t - 19 ) a(i) t = --------------------------------------- / 2 ----- (t - 1) (t - 1835575167554 t + 1) i = 0 infinity ----- 2 \ i 3 (428400628593 t + 605285045966 t + 1) ) b(i) t = - ---------------------------------------- / 2 ----- (t - 1) (t - 1835575167554 t + 1) i = 0 infinity ----- 2 \ i 3 (247461021971 t - 1281146696534 t + 3) ) c(i) t = ----------------------------------------- / 2 ----- (t - 1) (t - 1835575167554 t + 1) i = 0 In Maple notation, these generating functions are (2714094099341*t^2+8105149294406*t-19)/(t-1)/(t^2-1835575167554*t+1) -3*(428400628593*t^2+605285045966*t+1)/(t-1)/(t^2-1835575167554*t+1) 3*(247461021971*t^2-1281146696534*t+3)/(t-1)/(t^2-1835575167554*t+1) Then for all i>=0 we have 3 3 3 3 a(i) + 35 b(i) + 35 c(i) = -3993 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 103, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 11 (31370722926567642071 t + 39785457596825122730 t - 1) ) a(i) t = --------------------------------------------------------- / 2 ----- (t - 1) (t - 152396499470363244098 t + 1) i = 0 infinity ----- 2 \ i 3 (58022327590742883369 t - 3101304246434482090 t + 1) ) b(i) t = - ------------------------------------------------------- / 2 ----- (t - 1) (t - 152396499470363244098 t + 1) i = 0 infinity ----- 2 \ i 6 (20795022076508487809 t - 48255533748662688450 t + 1) ) c(i) t = -------------------------------------------------------- / 2 ----- (t - 1) (t - 152396499470363244098 t + 1) i = 0 In Maple notation, these generating functions are 11*(31370722926567642071*t^2+39785457596825122730*t-1)/(t-1)/(t^2-\ 152396499470363244098*t+1) -3*(58022327590742883369*t^2-3101304246434482090*t+1)/(t-1)/(t^2-\ 152396499470363244098*t+1) 6*(20795022076508487809*t^2-48255533748662688450*t+1)/(t-1)/(t^2-\ 152396499470363244098*t+1) Then for all i>=0 we have 3 3 3 3 a(i) + 37 b(i) + 37 c(i) = -3000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 104, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = ( / ----- i = 0 2 4121320105067939183907784529251 t + 5958257263449180357053216430778 t - 29 / 2 ) / ((t - 1) (t - 771911262344609394531166310402 t + 1)) / infinity ----- \ i ) b(i) t = - 6 / ----- i = 0 2 (328173535913489425038603919681 t + 79845338074459941686953840318 t + 1) / 2 / ((t - 1) (t - 771911262344609394531166310402 t + 1)) / infinity ----- \ i ) c(i) t = 15 / ----- i = 0 2 (85476968753529779083132850881 t - 248684518348709525773355954882 t + 1) / 2 / ((t - 1) (t - 771911262344609394531166310402 t + 1)) / In Maple notation, these generating functions are (4121320105067939183907784529251*t^2+5958257263449180357053216430778*t-29)/(t-1 )/(t^2-771911262344609394531166310402*t+1) -6*(328173535913489425038603919681*t^2+79845338074459941686953840318*t+1)/(t-1) /(t^2-771911262344609394531166310402*t+1) 15*(85476968753529779083132850881*t^2-248684518348709525773355954882*t+1)/(t-1) /(t^2-771911262344609394531166310402*t+1) Then for all i>=0 we have 3 3 3 3 a(i) + 38 b(i) + 38 c(i) = -46875 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 105, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 4 (9893 t + 352514 t - 7) ) a(i) t = ---------------------------- / 2 ----- (t - 1) (t - 1435202 t + 1) i = 0 infinity ----- 2 \ i 12 (1811 t + 16188 t + 1) ) b(i) t = - ---------------------------- / 2 ----- (t - 1) (t - 1435202 t + 1) i = 0 infinity ----- 2 \ i 15 (1185 t - 15586 t + 1) ) c(i) t = ---------------------------- / 2 ----- (t - 1) (t - 1435202 t + 1) i = 0 In Maple notation, these generating functions are 4*(9893*t^2+352514*t-7)/(t-1)/(t^2-1435202*t+1) -12*(1811*t^2+16188*t+1)/(t-1)/(t^2-1435202*t+1) 15*(1185*t^2-15586*t+1)/(t-1)/(t^2-1435202*t+1) Then for all i>=0 we have 3 3 3 3 a(i) + 40 b(i) + 40 c(i) = -24 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 106, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 6706609773179 t + 16962712723346 t - 13 ) a(i) t = ---------------------------------------- / 2 ----- (t - 1) (t - 5735670545474 t + 1) i = 0 infinity ----- 2 \ i 3 (1056936618585 t + 599127354278 t + 1) ) b(i) t = - ----------------------------------------- / 2 ----- (t - 1) (t - 5735670545474 t + 1) i = 0 infinity ----- 2 \ i 6 (368787124217 t - 1196819110650 t + 1) ) c(i) t = ----------------------------------------- / 2 ----- (t - 1) (t - 5735670545474 t + 1) i = 0 In Maple notation, these generating functions are (6706609773179*t^2+16962712723346*t-13)/(t-1)/(t^2-5735670545474*t+1) -3*(1056936618585*t^2+599127354278*t+1)/(t-1)/(t^2-5735670545474*t+1) 6*(368787124217*t^2-1196819110650*t+1)/(t-1)/(t^2-5735670545474*t+1) Then for all i>=0 we have 3 3 3 3 a(i) + 43 b(i) + 43 c(i) = -1536 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 107, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 14 (1436007875726950533592656478336338992886995 t / ----- i = 0 / + 5057800376321847848827448057453977332724814 t - 1) / ((t - 1) / 2 (t - 25069120228839547243761333789330058373292098 t + 1)) infinity ----- \ i 2 ) b(i) t = - 3 (2996427299501039368655807489985411937382785 t / ----- i = 0 / + 3346362155988484632777782986833036566703166 t + 1) / ((t - 1) / 2 (t - 25069120228839547243761333789330058373292098 t + 1)) infinity ----- \ i 2 ) c(i) t = 6 (1019544357841536173130351585547259637729061 t / ----- i = 0 / - 4190939085586298173847146823956483889772038 t + 1) / ((t - 1) / 2 (t - 25069120228839547243761333789330058373292098 t + 1)) In Maple notation, these generating functions are 14*(1436007875726950533592656478336338992886995*t^2+ 5057800376321847848827448057453977332724814*t-1)/(t-1)/(t^2-\ 25069120228839547243761333789330058373292098*t+1) -3*(2996427299501039368655807489985411937382785*t^2+ 3346362155988484632777782986833036566703166*t+1)/(t-1)/(t^2-\ 25069120228839547243761333789330058373292098*t+1) 6*(1019544357841536173130351585547259637729061*t^2-\ 4190939085586298173847146823956483889772038*t+1)/(t-1)/(t^2-\ 25069120228839547243761333789330058373292098*t+1) Then for all i>=0 we have 3 3 3 3 a(i) + 49 b(i) + 49 c(i) = -1029 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 108, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 3201860023158792078697 t + 274425465404719245314926 t - 23 ) a(i) t = ----------------------------------------------------------- / 2 ----- (t - 1) (t - 455920103225597877921602 t + 1) i = 0 infinity ----- \ i ) b(i) t = / ----- i = 0 2 3 (419226028165163754361 t + 30145250165729666050438 t + 1) - ------------------------------------------------------------ 2 (t - 1) (t - 455920103225597877921602 t + 1) infinity ----- 2 \ i 9 (50801453189532582601 t - 10238960184487809184202 t + 1) ) c(i) t = ----------------------------------------------------------- / 2 ----- (t - 1) (t - 455920103225597877921602 t + 1) i = 0 In Maple notation, these generating functions are (3201860023158792078697*t^2+274425465404719245314926*t-23)/(t-1)/(t^2-\ 455920103225597877921602*t+1) -3*(419226028165163754361*t^2+30145250165729666050438*t+1)/(t-1)/(t^2-\ 455920103225597877921602*t+1) 9*(50801453189532582601*t^2-10238960184487809184202*t+1)/(t-1)/(t^2-\ 455920103225597877921602*t+1) Then for all i>=0 we have 3 3 3 3 a(i) + 52 b(i) + 52 c(i) = -3 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 109, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 28 (59791789895 t + 252973394234 t - 1) ) a(i) t = ---------------------------------------- / 2 ----- (t - 1) (t - 1093216624898 t + 1) i = 0 infinity ----- 2 \ i 2 (325720145881 t + 963340098982 t + 1) ) b(i) t = - ---------------------------------------- / 2 ----- (t - 1) (t - 1093216624898 t + 1) i = 0 infinity ----- 2 \ i 292689552395 t - 2870810042134 t + 11 ) c(i) t = -------------------------------------- / 2 ----- (t - 1) (t - 1093216624898 t + 1) i = 0 In Maple notation, these generating functions are 28*(59791789895*t^2+252973394234*t-1)/(t-1)/(t^2-1093216624898*t+1) -2*(325720145881*t^2+963340098982*t+1)/(t-1)/(t^2-1093216624898*t+1) (292689552395*t^2-2870810042134*t+11)/(t-1)/(t^2-1093216624898*t+1) Then for all i>=0 we have 3 3 3 3 a(i) + 56 b(i) + 56 c(i) = -8232 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 110, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (493351583488691 t + 826026886323098 t - 13) ) a(i) t = ----------------------------------------------- / 2 ----- (t - 1) (t - 216248495052098 t + 1) i = 0 infinity ----- 2 \ i 2 (186144199988833 t + 160553792078494 t + 1) ) b(i) t = - ---------------------------------------------- / 2 ----- (t - 1) (t - 216248495052098 t + 1) i = 0 infinity ----- 2 \ i 11 (17025596015401 t - 80061594573098 t + 1) ) c(i) t = --------------------------------------------- / 2 ----- (t - 1) (t - 216248495052098 t + 1) i = 0 In Maple notation, these generating functions are 2*(493351583488691*t^2+826026886323098*t-13)/(t-1)/(t^2-216248495052098*t+1) -2*(186144199988833*t^2+160553792078494*t+1)/(t-1)/(t^2-216248495052098*t+1) 11*(17025596015401*t^2-80061594573098*t+1)/(t-1)/(t^2-216248495052098*t+1) Then for all i>=0 we have 3 3 3 3 a(i) + 64 b(i) + 64 c(i) = -31944 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 111, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (27514058064689908764234731680223377 t / ----- i = 0 / + 114628004901653380482244092265822726 t - 23) / ((t - 1) / 2 (t - 28021184309190457429899304311328322 t + 1)) infinity ----- \ i 2 ) b(i) t = - 6 (1937479650609385722052674948242161 t / ----- i = 0 / + 1262171152862189001776657377964878 t + 1) / ((t - 1) / 2 (t - 28021184309190457429899304311328322 t + 1)) infinity ----- \ i 2 ) c(i) t = 9 (1013733321975045948396381968724841 t / ----- i = 0 / - 3146833857622762430949270186196202 t + 1) / ((t - 1) / 2 (t - 28021184309190457429899304311328322 t + 1)) In Maple notation, these generating functions are (27514058064689908764234731680223377*t^2+114628004901653380482244092265822726*t -23)/(t-1)/(t^2-28021184309190457429899304311328322*t+1) -6*(1937479650609385722052674948242161*t^2+1262171152862189001776657377964878*t +1)/(t-1)/(t^2-28021184309190457429899304311328322*t+1) 9*(1013733321975045948396381968724841*t^2-3146833857622762430949270186196202*t+ 1)/(t-1)/(t^2-28021184309190457429899304311328322*t+1) Then for all i>=0 we have 3 3 3 3 a(i) + 77 b(i) + 77 c(i) = -3000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 112, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 2 ( / ----- i = 0 2 1039368870820739721128663155144626583913508894278580137180576211889 t + 1721757570434967840074553689946270907788688380225046632324646841722 t / 2 - 11) / ((t - 1) (t / - 642995510488884597706020769018690307164848843898349910833675841602 t + 1 )) infinity ----- \ i ) b(i) t = - 6 ( / ----- i = 0 2 144047220393570036853313310619564652566541955942476690278959384101 t - 38578139875477387600692882648413817917780257895815138848299541702 t + 1) / 2 / ((t - 1) (t / - 642995510488884597706020769018690307164848843898349910833675841602 t + 1 )) infinity ----- \ i ) c(i) t = 3 ( / ----- i = 0 2 234793473052743164930797741488122813650339866024513373523017424003 t - 445731634088928463436038597430424482947863262117836476384337108806 t + 3 / 2 ) / ((t - 1) (t / - 642995510488884597706020769018690307164848843898349910833675841602 t + 1 )) In Maple notation, these generating functions are 2*(1039368870820739721128663155144626583913508894278580137180576211889*t^2+ 1721757570434967840074553689946270907788688380225046632324646841722*t-11)/(t-1) /(t^2-642995510488884597706020769018690307164848843898349910833675841602*t+1) -6*(144047220393570036853313310619564652566541955942476690278959384101*t^2-\ 38578139875477387600692882648413817917780257895815138848299541702*t+1)/(t-1)/(t ^2-642995510488884597706020769018690307164848843898349910833675841602*t+1) 3*(234793473052743164930797741488122813650339866024513373523017424003*t^2-\ 445731634088928463436038597430424482947863262117836476384337108806*t+3)/(t-1)/( t^2-642995510488884597706020769018690307164848843898349910833675841602*t+1) Then for all i>=0 we have 3 3 3 3 a(i) + 91 b(i) + 91 c(i) = -14739 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 113, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 9 (14492669414797 t + 20013602298806 t - 3) ) a(i) t = -------------------------------------------- / 2 ----- (t - 1) (t - 26803379131202 t + 1) i = 0 infinity ----- 2 \ i 24 (6811135747681 t - 2948493391682 t + 1) ) b(i) t = - ------------------------------------------- / 2 ----- (t - 1) (t - 26803379131202 t + 1) i = 0 infinity ----- 2 \ i 2 (68690226498857 t - 115041934770874 t + 17) ) c(i) t = ---------------------------------------------- / 2 ----- (t - 1) (t - 26803379131202 t + 1) i = 0 In Maple notation, these generating functions are 9*(14492669414797*t^2+20013602298806*t-3)/(t-1)/(t^2-26803379131202*t+1) -24*(6811135747681*t^2-2948493391682*t+1)/(t-1)/(t^2-26803379131202*t+1) 2*(68690226498857*t^2-115041934770874*t+17)/(t-1)/(t^2-26803379131202*t+1) Then for all i>=0 we have 3 3 3 4 a(i) + 5 b(i) + 5 c(i) = -48668 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 114, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 4706277428522851 t + 10537895626211578 t - 29 ) a(i) t = ---------------------------------------------- / 2 ----- (t - 1) (t - 1572185782036802 t + 1) i = 0 infinity ----- 2 \ i 16 (292637212067341 t + 59829216943858 t + 1) ) b(i) t = - ---------------------------------------------- / 2 ----- (t - 1) (t - 1572185782036802 t + 1) i = 0 infinity ----- 2 \ i 28 (125200929855241 t - 326610317861642 t + 1) ) c(i) t = ----------------------------------------------- / 2 ----- (t - 1) (t - 1572185782036802 t + 1) i = 0 In Maple notation, these generating functions are (4706277428522851*t^2+10537895626211578*t-29)/(t-1)/(t^2-1572185782036802*t+1) -16*(292637212067341*t^2+59829216943858*t+1)/(t-1)/(t^2-1572185782036802*t+1) 28*(125200929855241*t^2-326610317861642*t+1)/(t-1)/(t^2-1572185782036802*t+1) Then for all i>=0 we have 3 3 3 4 a(i) + 7 b(i) + 7 c(i) = -27436 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 115, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (57476509 t + 713619502 t - 11) ) a(i) t = ---------------------------------- / 2 ----- (t - 1) (t - 533702402 t + 1) i = 0 infinity ----- 2 \ i 5 (18050761 t + 169091638 t + 1) ) b(i) t = - --------------------------------- / 2 ----- (t - 1) (t - 533702402 t + 1) i = 0 infinity ----- 2 \ i 39163577 t - 974875594 t + 17 ) c(i) t = ------------------------------ / 2 ----- (t - 1) (t - 533702402 t + 1) i = 0 In Maple notation, these generating functions are 2*(57476509*t^2+713619502*t-11)/(t-1)/(t^2-533702402*t+1) -5*(18050761*t^2+169091638*t+1)/(t-1)/(t^2-533702402*t+1) (39163577*t^2-974875594*t+17)/(t-1)/(t^2-533702402*t+1) Then for all i>=0 we have 3 3 3 4 a(i) + 9 b(i) + 9 c(i) = -500 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 116, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (2951109071 t + 27124815758 t - 13) ) a(i) t = -------------------------------------- / 2 ----- (t - 1) (t - 15587522498 t + 1) i = 0 infinity ----- 2 \ i 7 (631997101 t + 3764483602 t + 1) ) b(i) t = - ----------------------------------- / 2 ----- (t - 1) (t - 15587522498 t + 1) i = 0 infinity ----- 2 \ i 2277718567 t - 33053083514 t + 19 ) c(i) t = ---------------------------------- / 2 ----- (t - 1) (t - 15587522498 t + 1) i = 0 In Maple notation, these generating functions are 2*(2951109071*t^2+27124815758*t-13)/(t-1)/(t^2-15587522498*t+1) -7*(631997101*t^2+3764483602*t+1)/(t-1)/(t^2-15587522498*t+1) (2277718567*t^2-33053083514*t+19)/(t-1)/(t^2-15587522498*t+1) Then for all i>=0 we have 3 3 3 4 a(i) + 11 b(i) + 11 c(i) = -1372 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 117, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 27 (6782930439203796854220568905479447852399 t / ----- i = 0 / + 153084082805155399656975303681727157528402 t - 1) / ((t - 1) / 2 (t - 2813816937547268025293117501251670941012802 t + 1)) infinity ----- \ i 2 ) b(i) t = - 2 (69973975293913189994137926695000723545567 t / ----- i = 0 / + 567919033218061929089944126485478834870426 t + 7) / ((t - 1) / 2 (t - 2813816937547268025293117501251670941012802 t + 1)) infinity ----- \ i 2 ) c(i) t = 20 (5166006310806293848774239065020621434409 t / ----- i = 0 / - 68955307162003805757182444383068577276010 t + 1) / ((t - 1) / 2 (t - 2813816937547268025293117501251670941012802 t + 1)) In Maple notation, these generating functions are 27*(6782930439203796854220568905479447852399*t^2+ 153084082805155399656975303681727157528402*t-1)/(t-1)/(t^2-\ 2813816937547268025293117501251670941012802*t+1) -2*(69973975293913189994137926695000723545567*t^2+ 567919033218061929089944126485478834870426*t+7)/(t-1)/(t^2-\ 2813816937547268025293117501251670941012802*t+1) 20*(5166006310806293848774239065020621434409*t^2-\ 68955307162003805757182444383068577276010*t+1)/(t-1)/(t^2-\ 2813816937547268025293117501251670941012802*t+1) Then for all i>=0 we have 3 3 3 4 a(i) + 15 b(i) + 15 c(i) = -108 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 118, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (486785344140834328758044997338338259 t / ----- i = 0 / + 6445790806791122564305519299302320650 t - 29) / ((t - 1) / 2 (t - 2771232126740893793050830760343256898 t + 1)) infinity ----- \ i 2 ) b(i) t = - 10 (57634773190374847023291040699905179 t / ----- i = 0 / + 3508570293849934912937541942321122 t + 3) / ((t - 1) / 2 (t - 2771232126740893793050830760343256898 t + 1)) infinity ----- \ i 2 ) c(i) t = 32 (17116040621733253061032043973613129 t / ----- i = 0 / - 36223335460553497416103476049308850 t + 1) / ((t - 1) / 2 (t - 2771232126740893793050830760343256898 t + 1)) In Maple notation, these generating functions are (486785344140834328758044997338338259*t^2+6445790806791122564305519299302320650 *t-29)/(t-1)/(t^2-2771232126740893793050830760343256898*t+1) -10*(57634773190374847023291040699905179*t^2+3508570293849934912937541942321122 *t+3)/(t-1)/(t^2-2771232126740893793050830760343256898*t+1) 32*(17116040621733253061032043973613129*t^2-36223335460553497416103476049308850 *t+1)/(t-1)/(t^2-2771232126740893793050830760343256898*t+1) Then for all i>=0 we have 3 3 3 4 a(i) + 17 b(i) + 17 c(i) = -500 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 119, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 777607 t + 2427282 t - 25 ) a(i) t = --------------------------- / 2 ----- (t - 1) (t - 492802 t + 1) i = 0 infinity ----- 2 \ i 8 (114787 t - 83174 t + 3) ) b(i) t = - --------------------------- / 2 ----- (t - 1) (t - 492802 t + 1) i = 0 infinity ----- 2 \ i 26 (33745 t - 43474 t + 1) ) c(i) t = --------------------------- / 2 ----- (t - 1) (t - 492802 t + 1) i = 0 In Maple notation, these generating functions are (777607*t^2+2427282*t-25)/(t-1)/(t^2-492802*t+1) -8*(114787*t^2-83174*t+3)/(t-1)/(t^2-492802*t+1) 26*(33745*t^2-43474*t+1)/(t-1)/(t^2-492802*t+1) Then for all i>=0 we have 3 3 3 4 a(i) + 19 b(i) + 19 c(i) = -8788 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 120, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 26 (90719 t + 12274082 t - 1) ) a(i) t = ------------------------------ / 2 ----- (t - 1) (t - 462336002 t + 1) i = 0 infinity ----- 2 \ i 3 (454241 t + 57606558 t + 1) ) b(i) t = - ------------------------------ / 2 ----- (t - 1) (t - 462336002 t + 1) i = 0 infinity ----- 2 \ i 15 (20961 t - 11633122 t + 1) ) c(i) t = ------------------------------ / 2 ----- (t - 1) (t - 462336002 t + 1) i = 0 In Maple notation, these generating functions are 26*(90719*t^2+12274082*t-1)/(t-1)/(t^2-462336002*t+1) -3*(454241*t^2+57606558*t+1)/(t-1)/(t^2-462336002*t+1) 15*(20961*t^2-11633122*t+1)/(t-1)/(t^2-462336002*t+1) Then for all i>=0 we have 3 3 3 4 a(i) + 21 b(i) + 21 c(i) = -4 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 121, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (186166199376425 t + 431792442054878 t - 7) ) a(i) t = ---------------------------------------------- / 2 ----- (t - 1) (t - 268510893235202 t + 1) i = 0 infinity ----- 2 \ i 246528672098549 t + 71081355899654 t + 5 ) b(i) t = - ----------------------------------------- / 2 ----- (t - 1) (t - 268510893235202 t + 1) i = 0 infinity ----- 2 \ i 9 (20197245716209 t - 55487248827122 t + 1) ) c(i) t = -------------------------------------------- / 2 ----- (t - 1) (t - 268510893235202 t + 1) i = 0 In Maple notation, these generating functions are 2*(186166199376425*t^2+431792442054878*t-7)/(t-1)/(t^2-268510893235202*t+1) -(246528672098549*t^2+71081355899654*t+5)/(t-1)/(t^2-268510893235202*t+1) 9*(20197245716209*t^2-55487248827122*t+1)/(t-1)/(t^2-268510893235202*t+1) Then for all i>=0 we have 3 3 3 4 a(i) + 23 b(i) + 23 c(i) = -2916 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 122, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (1597991 t + 7854818 t - 9) ) a(i) t = ------------------------------ / 2 ----- (t - 1) (t - 5299202 t + 1) i = 0 infinity ----- 2 \ i 7 (299281 t + 340718 t + 1) ) b(i) t = - ---------------------------- / 2 ----- (t - 1) (t - 5299202 t + 1) i = 0 infinity ----- 2 \ i 1583611 t - 6063622 t + 11 ) c(i) t = ---------------------------- / 2 ----- (t - 1) (t - 5299202 t + 1) i = 0 In Maple notation, these generating functions are 2*(1597991*t^2+7854818*t-9)/(t-1)/(t^2-5299202*t+1) -7*(299281*t^2+340718*t+1)/(t-1)/(t^2-5299202*t+1) (1583611*t^2-6063622*t+11)/(t-1)/(t^2-5299202*t+1) Then for all i>=0 we have 3 3 3 4 a(i) + 25 b(i) + 25 c(i) = -1372 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 123, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 11290733 t + 14207654 t - 19 ) a(i) t = ----------------------------- / 2 ----- (t - 1) (t - 2979074 t + 1) i = 0 infinity ----- 2 \ i 2 (4072853 t - 1957786 t + 5) ) b(i) t = - ------------------------------ / 2 ----- (t - 1) (t - 2979074 t + 1) i = 0 infinity ----- 2 \ i 2 (3445591 t - 5560670 t + 7) ) c(i) t = ------------------------------ / 2 ----- (t - 1) (t - 2979074 t + 1) i = 0 In Maple notation, these generating functions are (11290733*t^2+14207654*t-19)/(t-1)/(t^2-2979074*t+1) -2*(4072853*t^2-1957786*t+5)/(t-1)/(t^2-2979074*t+1) 2*(3445591*t^2-5560670*t+7)/(t-1)/(t^2-2979074*t+1) Then for all i>=0 we have 3 3 3 4 a(i) + 27 b(i) + 27 c(i) = -19652 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 124, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2438617563173 t + 84192991064054 t - 27 ) a(i) t = ---------------------------------------- / 2 ----- (t - 1) (t - 85407133593602 t + 1) i = 0 infinity ----- 2 \ i 13 (120981907201 t + 1244778707198 t + 1) ) b(i) t = - ------------------------------------------ / 2 ----- (t - 1) (t - 85407133593602 t + 1) i = 0 infinity ----- 2 \ i 1236403750417 t - 18991291737634 t + 17 ) c(i) t = ---------------------------------------- / 2 ----- (t - 1) (t - 85407133593602 t + 1) i = 0 In Maple notation, these generating functions are (2438617563173*t^2+84192991064054*t-27)/(t-1)/(t^2-85407133593602*t+1) -13*(120981907201*t^2+1244778707198*t+1)/(t-1)/(t^2-85407133593602*t+1) (1236403750417*t^2-18991291737634*t+17)/(t-1)/(t^2-85407133593602*t+1) Then for all i>=0 we have 3 3 3 4 a(i) + 29 b(i) + 29 c(i) = -32 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 125, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 30 (93133805547765884452233271 t + 7388201155961751831650704650 t - 1) ----------------------------------------------------------------------- 2 (t - 1) (t - 443321211031864300576502265602 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 15 (119334875280493141641701897 t + 2752756565051334093023203062 t + 1) - ------------------------------------------------------------------------ 2 (t - 1) (t - 443321211031864300576502265602 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 19 (75237114328858072545201001 t - 2342677725117142731491178602 t + 1) ----------------------------------------------------------------------- 2 (t - 1) (t - 443321211031864300576502265602 t + 1) In Maple notation, these generating functions are 30*(93133805547765884452233271*t^2+7388201155961751831650704650*t-1)/(t-1)/(t^2 -443321211031864300576502265602*t+1) -15*(119334875280493141641701897*t^2+2752756565051334093023203062*t+1)/(t-1)/(t ^2-443321211031864300576502265602*t+1) 19*(75237114328858072545201001*t^2-2342677725117142731491178602*t+1)/(t-1)/(t^2 -443321211031864300576502265602*t+1) Then for all i>=0 we have 3 3 3 4 a(i) + 31 b(i) + 31 c(i) = -4 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 126, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 22 (2351579 t + 6111734 t - 1) ) a(i) t = ------------------------------- / 2 ----- (t - 1) (t - 28366274 t + 1) i = 0 infinity ----- 2 \ i 9 (3641837 t - 118318 t + 1) ) b(i) t = - ----------------------------- / 2 ----- (t - 1) (t - 28366274 t + 1) i = 0 infinity ----- 2 \ i 13 (2066461 t - 4505822 t + 1) ) c(i) t = ------------------------------- / 2 ----- (t - 1) (t - 28366274 t + 1) i = 0 In Maple notation, these generating functions are 22*(2351579*t^2+6111734*t-1)/(t-1)/(t^2-28366274*t+1) -9*(3641837*t^2-118318*t+1)/(t-1)/(t^2-28366274*t+1) 13*(2066461*t^2-4505822*t+1)/(t-1)/(t^2-28366274*t+1) Then for all i>=0 we have 3 3 3 4 a(i) + 35 b(i) + 35 c(i) = -8788 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 127, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (140758643 t + 603746714 t - 13) ) a(i) t = ----------------------------------- / 2 ----- (t - 1) (t - 268369922 t + 1) i = 0 infinity ----- 2 \ i 11 (16137601 t + 5685886 t + 1) ) b(i) t = - -------------------------------- / 2 ----- (t - 1) (t - 268369922 t + 1) i = 0 infinity ----- 2 \ i 3 (49026437 t - 129045898 t + 5) ) c(i) t = --------------------------------- / 2 ----- (t - 1) (t - 268369922 t + 1) i = 0 In Maple notation, these generating functions are 2*(140758643*t^2+603746714*t-13)/(t-1)/(t^2-268369922*t+1) -11*(16137601*t^2+5685886*t+1)/(t-1)/(t^2-268369922*t+1) 3*(49026437*t^2-129045898*t+5)/(t-1)/(t^2-268369922*t+1) Then for all i>=0 we have 3 3 3 4 a(i) + 37 b(i) + 37 c(i) = -5324 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 128, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (1051379469222905783 t + 2825335360259747750 t - 13) ) a(i) t = ------------------------------------------------------- / 2 ----- (t - 1) (t - 1026445749996828098 t + 1) i = 0 infinity ----- 2 \ i 1315156773442285799 t - 185882826665811250 t + 11 ) b(i) t = - -------------------------------------------------- / 2 ----- (t - 1) (t - 1026445749996828098 t + 1) i = 0 infinity ----- 2 \ i 15 (74000637329025157 t - 149285567114123462 t + 1) ) c(i) t = ---------------------------------------------------- / 2 ----- (t - 1) (t - 1026445749996828098 t + 1) i = 0 In Maple notation, these generating functions are 2*(1051379469222905783*t^2+2825335360259747750*t-13)/(t-1)/(t^2-\ 1026445749996828098*t+1) -(1315156773442285799*t^2-185882826665811250*t+11)/(t-1)/(t^2-\ 1026445749996828098*t+1) 15*(74000637329025157*t^2-149285567114123462*t+1)/(t-1)/(t^2-\ 1026445749996828098*t+1) Then for all i>=0 we have 3 3 3 4 a(i) + 41 b(i) + 41 c(i) = -13500 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 129, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 10 (482492677 t + 1992120766 t - 3) ) a(i) t = ------------------------------------ / 2 ----- (t - 1) (t - 3782496002 t + 1) i = 0 infinity ----- 2 \ i 13 (231313321 t + 33153878 t + 1) ) b(i) t = - ---------------------------------- / 2 ----- (t - 1) (t - 3782496002 t + 1) i = 0 infinity ----- 2 \ i 2558242777 t - 5996316394 t + 17 ) c(i) t = --------------------------------- / 2 ----- (t - 1) (t - 3782496002 t + 1) i = 0 In Maple notation, these generating functions are 10*(482492677*t^2+1992120766*t-3)/(t-1)/(t^2-3782496002*t+1) -13*(231313321*t^2+33153878*t+1)/(t-1)/(t^2-3782496002*t+1) (2558242777*t^2-5996316394*t+17)/(t-1)/(t^2-3782496002*t+1) Then for all i>=0 we have 3 3 3 4 a(i) + 43 b(i) + 43 c(i) = -8788 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 130, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 151171 t + 11388058 t - 29 ) a(i) t = ----------------------------- / 2 ----- (t - 1) (t - 23020802 t + 1) i = 0 infinity ----- 2 \ i 2 (52889 t + 523102 t + 9) ) b(i) t = - ----------------------------- / 2 ----- (t - 1) (t - 23020802 t + 1) i = 0 infinity ----- 2 \ i 20 (4785 t - 62386 t + 1) ) c(i) t = ----------------------------- / 2 ----- (t - 1) (t - 23020802 t + 1) i = 0 In Maple notation, these generating functions are (151171*t^2+11388058*t-29)/(t-1)/(t^2-23020802*t+1) -2*(52889*t^2+523102*t+9)/(t-1)/(t^2-23020802*t+1) 20*(4785*t^2-62386*t+1)/(t-1)/(t^2-23020802*t+1) Then for all i>=0 we have 3 3 3 4 a(i) + 45 b(i) + 45 c(i) = -4 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 131, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 6 (21505871587 t + 59272811362 t - 5) ) a(i) t = -------------------------------------- / 2 ----- (t - 1) (t - 56711612162 t + 1) i = 0 infinity ----- 2 \ i 79921904773 t - 18272138642 t + 13 ) b(i) t = - ----------------------------------- / 2 ----- (t - 1) (t - 56711612162 t + 1) i = 0 infinity ----- 2 \ i 17 (4055304889 t - 7681761722 t + 1) ) c(i) t = ------------------------------------- / 2 ----- (t - 1) (t - 56711612162 t + 1) i = 0 In Maple notation, these generating functions are 6*(21505871587*t^2+59272811362*t-5)/(t-1)/(t^2-56711612162*t+1) -(79921904773*t^2-18272138642*t+13)/(t-1)/(t^2-56711612162*t+1) 17*(4055304889*t^2-7681761722*t+1)/(t-1)/(t^2-56711612162*t+1) Then for all i>=0 we have 3 3 3 4 a(i) + 47 b(i) + 47 c(i) = -19652 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 132, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 21 (232218228479 t + 1425174784322 t - 1) ) a(i) t = ------------------------------------------ / 2 ----- (t - 1) (t - 9682664443202 t + 1) i = 0 infinity ----- 2 \ i 6 (411186641881 t + 810050314918 t + 1) ) b(i) t = - ---------------------------------------- / 2 ----- (t - 1) (t - 9682664443202 t + 1) i = 0 infinity ----- 2 \ i 10 (177046516585 t - 909788690666 t + 1) ) c(i) t = ----------------------------------------- / 2 ----- (t - 1) (t - 9682664443202 t + 1) i = 0 In Maple notation, these generating functions are 21*(232218228479*t^2+1425174784322*t-1)/(t-1)/(t^2-9682664443202*t+1) -6*(411186641881*t^2+810050314918*t+1)/(t-1)/(t^2-9682664443202*t+1) 10*(177046516585*t^2-909788690666*t+1)/(t-1)/(t^2-9682664443202*t+1) Then for all i>=0 we have 3 3 3 4 a(i) + 49 b(i) + 49 c(i) = -1372 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 133, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 30 ( / ----- i = 0 2 2602509335991863130147077982795 t + 2802437620957237009717276467526 t - 1) / 2 / ((t - 1) (t - 11144187487361473707301782206402 t + 1)) / infinity ----- \ i ) b(i) t = - 15 ( / ----- i = 0 2 3179833162333246927125512053853 t - 2083042550261030561684422070814 t + 1) / 2 / ((t - 1) (t - 11144187487361473707301782206402 t + 1)) / infinity ----- \ i 2 ) c(i) t = (42404258107557626354041166266519 t / ----- i = 0 / - 58856117288640871835657516012138 t + 19) / ((t - 1) / 2 (t - 11144187487361473707301782206402 t + 1)) In Maple notation, these generating functions are 30*(2602509335991863130147077982795*t^2+2802437620957237009717276467526*t-1)/(t -1)/(t^2-11144187487361473707301782206402*t+1) -15*(3179833162333246927125512053853*t^2-2083042550261030561684422070814*t+1)/( t-1)/(t^2-11144187487361473707301782206402*t+1) (42404258107557626354041166266519*t^2-58856117288640871835657516012138*t+19)/(t -1)/(t^2-11144187487361473707301782206402*t+1) Then for all i>=0 we have 3 3 3 4 a(i) + 59 b(i) + 59 c(i) = -97556 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 134, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 2444320876906707782931239 t + 7297934747023571177911970 t - 9 -------------------------------------------------------------- 2 (t - 1) (t - 3769784047848101527308098 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 2 (562692110659695320710009 t + 458421313024975629196550 t + 1) - ---------------------------------------------------------------- 2 (t - 1) (t - 3769784047848101527308098 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 4 (194048881154608096678889 t - 704605592996943571632170 t + 1) ---------------------------------------------------------------- 2 (t - 1) (t - 3769784047848101527308098 t + 1) In Maple notation, these generating functions are (2444320876906707782931239*t^2+7297934747023571177911970*t-9)/(t-1)/(t^2-\ 3769784047848101527308098*t+1) -2*(562692110659695320710009*t^2+458421313024975629196550*t+1)/(t-1)/(t^2-\ 3769784047848101527308098*t+1) 4*(194048881154608096678889*t^2-704605592996943571632170*t+1)/(t-1)/(t^2-\ 3769784047848101527308098*t+1) Then for all i>=0 we have 3 3 3 4 a(i) + 61 b(i) + 61 c(i) = -500 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 135, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 5 (5114919646363 t + 12006061540714 t - 5) ) a(i) t = ------------------------------------------- / 2 ----- (t - 1) (t - 9291462276098 t + 1) i = 0 infinity ----- 2 \ i 3 (3614585865073 t + 4117470154894 t + 1) ) b(i) t = - ------------------------------------------ / 2 ----- (t - 1) (t - 9291462276098 t + 1) i = 0 infinity ----- 2 \ i 5972405551067 t - 29168573610982 t + 11 ) c(i) t = ---------------------------------------- / 2 ----- (t - 1) (t - 9291462276098 t + 1) i = 0 In Maple notation, these generating functions are 5*(5114919646363*t^2+12006061540714*t-5)/(t-1)/(t^2-9291462276098*t+1) -3*(3614585865073*t^2+4117470154894*t+1)/(t-1)/(t^2-9291462276098*t+1) (5972405551067*t^2-29168573610982*t+11)/(t-1)/(t^2-9291462276098*t+1) Then for all i>=0 we have 3 3 3 4 a(i) + 63 b(i) + 63 c(i) = -19652 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 136, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 21 (958401599 t + 1398571202 t - 1) ) a(i) t = ------------------------------------ / 2 ----- (t - 1) (t - 4733164802 t + 1) i = 0 infinity ----- 2 \ i 2 (4176327121 t + 2795000878 t + 1) ) b(i) t = - ------------------------------------ / 2 ----- (t - 1) (t - 4733164802 t + 1) i = 0 infinity ----- 2 \ i 10 (432736753 t - 1827002354 t + 1) ) c(i) t = ------------------------------------ / 2 ----- (t - 1) (t - 4733164802 t + 1) i = 0 In Maple notation, these generating functions are 21*(958401599*t^2+1398571202*t-1)/(t-1)/(t^2-4733164802*t+1) -2*(4176327121*t^2+2795000878*t+1)/(t-1)/(t^2-4733164802*t+1) 10*(432736753*t^2-1827002354*t+1)/(t-1)/(t^2-4733164802*t+1) Then for all i>=0 we have 3 3 3 4 a(i) + 65 b(i) + 65 c(i) = -27436 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 137, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 13 (425059086688439576488182275857481954351 t / ----- i = 0 / + 852841627648575555158698479311955496850 t - 1) / ((t - 1) / 2 (t - 3651956263638669909550863669217547916098 t + 1)) infinity ----- \ i 2 ) b(i) t = - 4 (664612590969900440636083650154648740553 t / ----- i = 0 / - 102336276661613782711456117880096262026 t + 1) / ((t - 1) / 2 (t - 3651956263638669909550863669217547916098 t + 1)) infinity ----- \ i 2 ) c(i) t = 6 (359351301147362195358201682131170896633 t / ----- i = 0 / - 734202177352886633974620036980872548986 t + 1) / ((t - 1) / 2 (t - 3651956263638669909550863669217547916098 t + 1)) In Maple notation, these generating functions are 13*(425059086688439576488182275857481954351*t^2+ 852841627648575555158698479311955496850*t-1)/(t-1)/(t^2-\ 3651956263638669909550863669217547916098*t+1) -4*(664612590969900440636083650154648740553*t^2-\ 102336276661613782711456117880096262026*t+1)/(t-1)/(t^2-\ 3651956263638669909550863669217547916098*t+1) 6*(359351301147362195358201682131170896633*t^2-\ 734202177352886633974620036980872548986*t+1)/(t-1)/(t^2-\ 3651956263638669909550863669217547916098*t+1) Then for all i>=0 we have 3 3 3 4 a(i) + 77 b(i) + 77 c(i) = -2916 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 138, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 26978955521737 t + 384514759268686 t - 23 ) a(i) t = ------------------------------------------ / 2 ----- (t - 1) (t - 195910354252802 t + 1) i = 0 infinity ----- 2 \ i 5 (2183420571553 t + 15522285084766 t + 1) ) b(i) t = - ------------------------------------------- / 2 ----- (t - 1) (t - 195910354252802 t + 1) i = 0 infinity ----- 2 \ i 9 (768913395361 t - 10605416537762 t + 1) ) c(i) t = ------------------------------------------ / 2 ----- (t - 1) (t - 195910354252802 t + 1) i = 0 In Maple notation, these generating functions are (26978955521737*t^2+384514759268686*t-23)/(t-1)/(t^2-195910354252802*t+1) -5*(2183420571553*t^2+15522285084766*t+1)/(t-1)/(t^2-195910354252802*t+1) 9*(768913395361*t^2-10605416537762*t+1)/(t-1)/(t^2-195910354252802*t+1) Then for all i>=0 we have 3 3 3 4 a(i) + 81 b(i) + 81 c(i) = -256 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 139, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (13905647639305520987865780904069804787970095030383 t / ----- i = 0 / + 230779763749872573408087728646390735764346302851234 t - 17) / ((t - 1) / 2 (t - 141895192906053050174822354853463418493809052652802 t + 1)) infinity ----- \ i 2 ) b(i) t = - 2 (2492854341073276452162660857643193738745297097841 t / ----- i = 0 / + 31025695164293585793858367847899346062941880694158 t + 1) / ((t - 1) / 2 (t - 141895192906053050174822354853463418493809052652802 t + 1)) infinity ----- \ i 2 ) c(i) t = 6 (367429859047574784458694255745404419982762531601 t / ----- i = 0 / - 11540279694169862199799037157592917687211821795602 t + 1) / ((t - 1) / 2 (t - 141895192906053050174822354853463418493809052652802 t + 1)) In Maple notation, these generating functions are (13905647639305520987865780904069804787970095030383*t^2+ 230779763749872573408087728646390735764346302851234*t-17)/(t-1)/(t^2-\ 141895192906053050174822354853463418493809052652802*t+1) -2*(2492854341073276452162660857643193738745297097841*t^2+ 31025695164293585793858367847899346062941880694158*t+1)/(t-1)/(t^2-\ 141895192906053050174822354853463418493809052652802*t+1) 6*(367429859047574784458694255745404419982762531601*t^2-\ 11540279694169862199799037157592917687211821795602*t+1)/(t-1)/(t^2-\ 141895192906053050174822354853463418493809052652802*t+1) Then for all i>=0 we have 3 3 3 4 a(i) + 95 b(i) + 95 c(i) = -108 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 140, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 239971518935251 t + 4334413049295178 t - 29 ) a(i) t = -------------------------------------------- / 2 ----- (t - 1) (t - 2213213018860802 t + 1) i = 0 infinity ----- 2 \ i 94092294851287 t + 719679622947106 t + 7 ) b(i) t = - ----------------------------------------- / 2 ----- (t - 1) (t - 2213213018860802 t + 1) i = 0 infinity ----- 2 \ i 11 (5909530728241 t - 79888795982642 t + 1) ) c(i) t = -------------------------------------------- / 2 ----- (t - 1) (t - 2213213018860802 t + 1) i = 0 In Maple notation, these generating functions are (239971518935251*t^2+4334413049295178*t-29)/(t-1)/(t^2-2213213018860802*t+1) -(94092294851287*t^2+719679622947106*t+7)/(t-1)/(t^2-2213213018860802*t+1) 11*(5909530728241*t^2-79888795982642*t+1)/(t-1)/(t^2-2213213018860802*t+1) Then for all i>=0 we have 3 3 3 4 a(i) + 99 b(i) + 99 c(i) = -256 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 141, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 239743 t + 37473874 t - 17 ) a(i) t = ----------------------------- / 2 ----- (t - 1) (t - 46267202 t + 1) i = 0 infinity ----- 2 \ i 225721 t + 34766278 t + 1 ) b(i) t = - ----------------------------- / 2 ----- (t - 1) (t - 46267202 t + 1) i = 0 infinity ----- 2 \ i 16 (1621 t - 2188622 t + 1) ) c(i) t = ----------------------------- / 2 ----- (t - 1) (t - 46267202 t + 1) i = 0 In Maple notation, these generating functions are (239743*t^2+37473874*t-17)/(t-1)/(t^2-46267202*t+1) -(225721*t^2+34766278*t+1)/(t-1)/(t^2-46267202*t+1) 16*(1621*t^2-2188622*t+1)/(t-1)/(t^2-46267202*t+1) Then for all i>=0 we have 3 3 3 5 a(i) + 6 b(i) + 6 c(i) = -5 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 142, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 15931 t + 377698 t - 29 ) a(i) t = -------------------------- / 2 ----- (t - 1) (t - 91202 t + 1) i = 0 infinity ----- 2 \ i 14281 t + 321718 t + 1 ) b(i) t = - -------------------------- / 2 ----- (t - 1) (t - 91202 t + 1) i = 0 infinity ----- 2 \ i 2 (1453 t - 169466 t + 13) ) c(i) t = --------------------------- / 2 ----- (t - 1) (t - 91202 t + 1) i = 0 In Maple notation, these generating functions are (15931*t^2+377698*t-29)/(t-1)/(t^2-91202*t+1) -(14281*t^2+321718*t+1)/(t-1)/(t^2-91202*t+1) 2*(1453*t^2-169466*t+13)/(t-1)/(t^2-91202*t+1) Then for all i>=0 we have 3 3 3 5 a(i) + 7 b(i) + 7 c(i) = -1080 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 143, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 2 ( / ----- i = 0 2 960783033491359878045453534727244278208780492252833476977986173131029 t + 1283564132039826381235774340545885384317513010473859254149816843316982 t / 2 - 11) / ((t - 1) (t / - 425194884946625582454544859070732159693799908322483137669360149529602 t + 1)) infinity ----- \ i ) b(i) t = - 8 ( / ----- i = 0 2 224665559339866299779329493433346273295355492536430656453890606547161 t + 65347655615376650391504277369352443645014712193548098359564952012838 t / 2 + 1) / ((t - 1) (t / - 425194884946625582454544859070732159693799908322483137669360149529602 t + 1)) infinity ----- \ i ) c(i) t = 23 ( / ----- i = 0 2 48306559972519958990156422103299192009291957271900306686508963360161 t - 149180721696082724266968168469455267466812028482327699665102201120162 t / 2 + 1) / ((t - 1) (t / - 425194884946625582454544859070732159693799908322483137669360149529602 t + 1)) In Maple notation, these generating functions are 2*(960783033491359878045453534727244278208780492252833476977986173131029*t^2+ 1283564132039826381235774340545885384317513010473859254149816843316982*t-11)/(t -1)/(t^2-425194884946625582454544859070732159693799908322483137669360149529602* t+1) -8*(224665559339866299779329493433346273295355492536430656453890606547161*t^2+ 65347655615376650391504277369352443645014712193548098359564952012838*t+1)/(t-1) /(t^2-425194884946625582454544859070732159693799908322483137669360149529602*t+1 ) 23*(48306559972519958990156422103299192009291957271900306686508963360161*t^2-\ 149180721696082724266968168469455267466812028482327699665102201120162*t+1)/(t-1 )/(t^2-425194884946625582454544859070732159693799908322483137669360149529602*t+ 1) Then for all i>=0 we have 3 3 3 5 a(i) + 8 b(i) + 8 c(i) = -40000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 144, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (533323856952370004014452230636135977702784995 t / ----- i = 0 / + 1370635039654916423683408940326458317259276346 t - 29) / ((t - 1) / 2 (t - 182041109275410348189359265220075609465552898 t + 1)) infinity ----- \ i 2 ) b(i) t = - 6 (76803927327422028984600250994693672649612289 t / ----- i = 0 / + 109402321729525298907611110468640732725650430 t + 1) / ((t - 1) / 2 (t - 182041109275410348189359265220075609465552898 t + 1)) infinity ----- \ i 2 ) c(i) t = 2 (119302645117189002784123204934886022594089997 t / ----- i = 0 / - 677921392288030986460757289324889238719878170 t + 13) / ((t - 1) / 2 (t - 182041109275410348189359265220075609465552898 t + 1)) In Maple notation, these generating functions are (533323856952370004014452230636135977702784995*t^2+ 1370635039654916423683408940326458317259276346*t-29)/(t-1)/(t^2-\ 182041109275410348189359265220075609465552898*t+1) -6*(76803927327422028984600250994693672649612289*t^2+ 109402321729525298907611110468640732725650430*t+1)/(t-1)/(t^2-\ 182041109275410348189359265220075609465552898*t+1) 2*(119302645117189002784123204934886022594089997*t^2-\ 677921392288030986460757289324889238719878170*t+13)/(t-1)/(t^2-\ 182041109275410348189359265220075609465552898*t+1) Then for all i>=0 we have 3 3 3 5 a(i) + 9 b(i) + 9 c(i) = -34295 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 145, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 25293627334926914552143 t + 38115090163807169953474 t - 17 ) a(i) t = ----------------------------------------------------------- / 2 ----- (t - 1) (t - 6812874843613985203202 t + 1) i = 0 infinity ----- 2 \ i 19969683097517089141921 t + 19215479401700603530078 t + 1 ) b(i) t = - ---------------------------------------------------------- / 2 ----- (t - 1) (t - 6812874843613985203202 t + 1) i = 0 infinity ----- 2 \ i 16 (529536235216212544321 t - 2978608891417318336322 t + 1) ) c(i) t = ------------------------------------------------------------ / 2 ----- (t - 1) (t - 6812874843613985203202 t + 1) i = 0 In Maple notation, these generating functions are (25293627334926914552143*t^2+38115090163807169953474*t-17)/(t-1)/(t^2-\ 6812874843613985203202*t+1) -(19969683097517089141921*t^2+19215479401700603530078*t+1)/(t-1)/(t^2-\ 6812874843613985203202*t+1) 16*(529536235216212544321*t^2-2978608891417318336322*t+1)/(t-1)/(t^2-\ 6812874843613985203202*t+1) Then for all i>=0 we have 3 3 3 5 a(i) + 11 b(i) + 11 c(i) = -20480 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 146, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2717431678612990051 t + 30298145374923189178 t - 29 ) a(i) t = ---------------------------------------------------- / 2 ----- (t - 1) (t - 8302867620492211202 t + 1) i = 0 infinity ----- 2 \ i 7 (300088043686882081 t + 2412282503842333918 t + 1) ) b(i) t = - ----------------------------------------------------- / 2 ----- (t - 1) (t - 8302867620492211202 t + 1) i = 0 infinity ----- 2 \ i 2 (484176553193047691 t - 9977473469545303702 t + 11) ) c(i) t = ------------------------------------------------------ / 2 ----- (t - 1) (t - 8302867620492211202 t + 1) i = 0 In Maple notation, these generating functions are (2717431678612990051*t^2+30298145374923189178*t-29)/(t-1)/(t^2-\ 8302867620492211202*t+1) -7*(300088043686882081*t^2+2412282503842333918*t+1)/(t-1)/(t^2-\ 8302867620492211202*t+1) 2*(484176553193047691*t^2-9977473469545303702*t+11)/(t-1)/(t^2-\ 8302867620492211202*t+1) Then for all i>=0 we have 3 3 3 5 a(i) + 12 b(i) + 12 c(i) = -1715 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 147, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (711920003 t + 4703986250 t - 13) ) a(i) t = ------------------------------------ / 2 ----- (t - 1) (t - 1829272898 t + 1) i = 0 infinity ----- 2 \ i 3 (329215609 t + 1693321990 t + 1) ) b(i) t = - ----------------------------------- / 2 ----- (t - 1) (t - 1829272898 t + 1) i = 0 infinity ----- 2 \ i 18 (21910009 t - 358999610 t + 1) ) c(i) t = ---------------------------------- / 2 ----- (t - 1) (t - 1829272898 t + 1) i = 0 In Maple notation, these generating functions are 2*(711920003*t^2+4703986250*t-13)/(t-1)/(t^2-1829272898*t+1) -3*(329215609*t^2+1693321990*t+1)/(t-1)/(t^2-1829272898*t+1) 18*(21910009*t^2-358999610*t+1)/(t-1)/(t^2-1829272898*t+1) Then for all i>=0 we have 3 3 3 5 a(i) + 16 b(i) + 16 c(i) = -5000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 148, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 881659 t + 1665442 t - 29 ) a(i) t = --------------------------- / 2 ----- (t - 1) (t - 217154 t + 1) i = 0 infinity ----- 2 \ i 633151 t + 443962 t + 7 ) b(i) t = - --------------------------- / 2 ----- (t - 1) (t - 217154 t + 1) i = 0 infinity ----- 2 \ i 22 (16993 t - 65954 t + 1) ) c(i) t = --------------------------- / 2 ----- (t - 1) (t - 217154 t + 1) i = 0 In Maple notation, these generating functions are (881659*t^2+1665442*t-29)/(t-1)/(t^2-217154*t+1) -(633151*t^2+443962*t+7)/(t-1)/(t^2-217154*t+1) 22*(16993*t^2-65954*t+1)/(t-1)/(t^2-217154*t+1) Then for all i>=0 we have 3 3 3 5 a(i) + 17 b(i) + 17 c(i) = -53240 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 149, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 12119721588825996404508467 t + 25561636624708287045117146 t - 13 ----------------------------------------------------------------- 2 (t - 1) (t - 8057410265868190183756802 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 4 (2082309950989489255784641 t + 1048316486690851514199358 t + 1) - ------------------------------------------------------------------ 2 (t - 1) (t - 8057410265868190183756802 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 9 (619417513853257941851041 t - 2010807041711187172955042 t + 1) ----------------------------------------------------------------- 2 (t - 1) (t - 8057410265868190183756802 t + 1) In Maple notation, these generating functions are (12119721588825996404508467*t^2+25561636624708287045117146*t-13)/(t-1)/(t^2-\ 8057410265868190183756802*t+1) -4*(2082309950989489255784641*t^2+1048316486690851514199358*t+1)/(t-1)/(t^2-\ 8057410265868190183756802*t+1) 9*(619417513853257941851041*t^2-2010807041711187172955042*t+1)/(t-1)/(t^2-\ 8057410265868190183756802*t+1) Then for all i>=0 we have 3 3 3 5 a(i) + 22 b(i) + 22 c(i) = -3645 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 150, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 3 (59242473 t + 1618107934 t - 7) ) a(i) t = ---------------------------------- / 2 ----- (t - 1) (t - 4857811202 t + 1) i = 0 infinity ----- 2 \ i 3 (40440403 t + 493895594 t + 3) ) b(i) t = - --------------------------------- / 2 ----- (t - 1) (t - 4857811202 t + 1) i = 0 infinity ----- 2 \ i 2 (41342407 t - 842846414 t + 7) ) c(i) t = --------------------------------- / 2 ----- (t - 1) (t - 4857811202 t + 1) i = 0 In Maple notation, these generating functions are 3*(59242473*t^2+1618107934*t-7)/(t-1)/(t^2-4857811202*t+1) -3*(40440403*t^2+493895594*t+3)/(t-1)/(t^2-4857811202*t+1) 2*(41342407*t^2-842846414*t+7)/(t-1)/(t^2-4857811202*t+1) Then for all i>=0 we have 3 3 3 5 a(i) + 23 b(i) + 23 c(i) = -40 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 151, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 24 (3578651 t + 8256422 t - 1) ) a(i) t = ------------------------------- / 2 ----- (t - 1) (t - 26894594 t + 1) i = 0 infinity ----- 2 \ i 52160257 t + 85008382 t + 1 ) b(i) t = - ----------------------------- / 2 ----- (t - 1) (t - 26894594 t + 1) i = 0 infinity ----- 2 \ i 16 (1342882 t - 9915923 t + 1) ) c(i) t = ------------------------------- / 2 ----- (t - 1) (t - 26894594 t + 1) i = 0 In Maple notation, these generating functions are 24*(3578651*t^2+8256422*t-1)/(t-1)/(t^2-26894594*t+1) -(52160257*t^2+85008382*t+1)/(t-1)/(t^2-26894594*t+1) 16*(1342882*t^2-9915923*t+1)/(t-1)/(t^2-26894594*t+1) Then for all i>=0 we have 3 3 3 5 a(i) + 24 b(i) + 24 c(i) = -29160 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 152, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 83789150928007725181 t + 450232034536925594838 t - 19 ) a(i) t = ------------------------------------------------------ / 2 ----- (t - 1) (t - 148422321388168520002 t + 1) i = 0 infinity ----- 2 \ i 7 (8029741207512070201 t + 13577091693341129798 t + 1) ) b(i) t = - ------------------------------------------------------- / 2 ----- (t - 1) (t - 148422321388168520002 t + 1) i = 0 infinity ----- 2 \ i 4 (10023722549299597603 t - 47835680125792697606 t + 3) ) c(i) t = -------------------------------------------------------- / 2 ----- (t - 1) (t - 148422321388168520002 t + 1) i = 0 In Maple notation, these generating functions are (83789150928007725181*t^2+450232034536925594838*t-19)/(t-1)/(t^2-\ 148422321388168520002*t+1) -7*(8029741207512070201*t^2+13577091693341129798*t+1)/(t-1)/(t^2-\ 148422321388168520002*t+1) 4*(10023722549299597603*t^2-47835680125792697606*t+3)/(t-1)/(t^2-\ 148422321388168520002*t+1) Then for all i>=0 we have 3 3 3 5 a(i) + 26 b(i) + 26 c(i) = -1715 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 153, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 24 (3230525864377289383520910757647314034500224811 t / ----- i = 0 / + 7652545875856524076110148463501245679227248470 t - 1) / ((t - 1) / 2 (t - 34530294694607434205656292176483305280432260098 t + 1)) infinity ----- \ i 2 ) b(i) t = - 12 (4891039059574042923050641185702678692892421129 t / ----- i = 0 / - 728922915424881405337020438080803626995288330 t + 1) / ((t - 1) / 2 (t - 34530294694607434205656292176483305280432260098 t + 1)) infinity ----- \ i 2 ) c(i) t = (48752389132189163127312584204901947285477592593 t / ----- i = 0 / - 98697782861979101339876033176364448076243186210 t + 17) / ((t - 1) / 2 (t - 34530294694607434205656292176483305280432260098 t + 1)) In Maple notation, these generating functions are 24*(3230525864377289383520910757647314034500224811*t^2+ 7652545875856524076110148463501245679227248470*t-1)/(t-1)/(t^2-\ 34530294694607434205656292176483305280432260098*t+1) -12*(4891039059574042923050641185702678692892421129*t^2-\ 728922915424881405337020438080803626995288330*t+1)/(t-1)/(t^2-\ 34530294694607434205656292176483305280432260098*t+1) (48752389132189163127312584204901947285477592593*t^2-\ 98697782861979101339876033176364448076243186210*t+17)/(t-1)/(t^2-\ 34530294694607434205656292176483305280432260098*t+1) Then for all i>=0 we have 3 3 3 5 a(i) + 27 b(i) + 27 c(i) = -16875 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 154, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 518027715904983008463662543 t + 1191279024083272185628243074 t - 17 -------------------------------------------------------------------- 2 (t - 1) (t - 303467058614590076403579202 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 2 (172070696494629353062620163 t + 53261642110225380621811834 t + 3) - --------------------------------------------------------------------- 2 (t - 1) (t - 303467058614590076403579202 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 11 (22876040338228340029832521 t - 63845556448201927972456522 t + 1) --------------------------------------------------------------------- 2 (t - 1) (t - 303467058614590076403579202 t + 1) In Maple notation, these generating functions are (518027715904983008463662543*t^2+1191279024083272185628243074*t-17)/(t-1)/(t^2-\ 303467058614590076403579202*t+1) -2*(172070696494629353062620163*t^2+53261642110225380621811834*t+3)/(t-1)/(t^2-\ 303467058614590076403579202*t+1) 11*(22876040338228340029832521*t^2-63845556448201927972456522*t+1)/(t-1)/(t^2-\ 303467058614590076403579202*t+1) Then for all i>=0 we have 3 3 3 5 a(i) + 28 b(i) + 28 c(i) = -6655 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 155, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 7 (189534025853 t + 963696019334 t - 3) ) a(i) t = ---------------------------------------- / 2 ----- (t - 1) (t - 1973817065474 t + 1) i = 0 infinity ----- 2 \ i 8 (109689379073 t + 147456599806 t + 1) ) b(i) t = - ---------------------------------------- / 2 ----- (t - 1) (t - 1973817065474 t + 1) i = 0 infinity ----- 2 \ i 648767070349 t - 2705934901402 t + 13 ) c(i) t = -------------------------------------- / 2 ----- (t - 1) (t - 1973817065474 t + 1) i = 0 In Maple notation, these generating functions are 7*(189534025853*t^2+963696019334*t-3)/(t-1)/(t^2-1973817065474*t+1) -8*(109689379073*t^2+147456599806*t+1)/(t-1)/(t^2-1973817065474*t+1) (648767070349*t^2-2705934901402*t+13)/(t-1)/(t^2-1973817065474*t+1) Then for all i>=0 we have 3 3 3 5 a(i) + 29 b(i) + 29 c(i) = -2560 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 156, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 30 (2713466715162565163880275236268496924268655 t / ----- i = 0 / + 191873897067731488383280902976397348065409426 t - 1) / ((t - 1) / 2 (t - 2510606680984342835987032236245436296554521602 t + 1)) infinity ----- \ i 2 ) b(i) t = - (43444758595682402601054098336907464295050881 t / ----- i = 0 / + 2995064549686101714302566823280429862830837118 t + 1) / ((t - 1) / 2 (t - 2510606680984342835987032236245436296554521602 t + 1)) infinity ----- \ i 2 ) c(i) t = 16 (402683734534782125167919296964247548893531 t / ----- i = 0 / - 190309515502146289431644226898047830494261532 t + 1) / ((t - 1) / 2 (t - 2510606680984342835987032236245436296554521602 t + 1)) In Maple notation, these generating functions are 30*(2713466715162565163880275236268496924268655*t^2+ 191873897067731488383280902976397348065409426*t-1)/(t-1)/(t^2-\ 2510606680984342835987032236245436296554521602*t+1) -(43444758595682402601054098336907464295050881*t^2+ 2995064549686101714302566823280429862830837118*t+1)/(t-1)/(t^2-\ 2510606680984342835987032236245436296554521602*t+1) 16*(402683734534782125167919296964247548893531*t^2-\ 190309515502146289431644226898047830494261532*t+1)/(t-1)/(t^2-\ 2510606680984342835987032236245436296554521602*t+1) Then for all i>=0 we have 3 3 3 5 a(i) + 33 b(i) + 33 c(i) = -135 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 157, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 3 (11135026853467913 t + 27157500974226494 t - 7) ) a(i) t = -------------------------------------------------- / 2 ----- (t - 1) (t - 17389882045972802 t + 1) i = 0 infinity ----- 2 \ i 8 (2711310093818041 t + 422385219423958 t + 1) ) b(i) t = - ----------------------------------------------- / 2 ----- (t - 1) (t - 17389882045972802 t + 1) i = 0 infinity ----- 2 \ i 13 (1290612992571241 t - 3219040877643242 t + 1) ) c(i) t = ------------------------------------------------- / 2 ----- (t - 1) (t - 17389882045972802 t + 1) i = 0 In Maple notation, these generating functions are 3*(11135026853467913*t^2+27157500974226494*t-7)/(t-1)/(t^2-17389882045972802*t+ 1) -8*(2711310093818041*t^2+422385219423958*t+1)/(t-1)/(t^2-17389882045972802*t+1) 13*(1290612992571241*t^2-3219040877643242*t+1)/(t-1)/(t^2-17389882045972802*t+1 ) Then for all i>=0 we have 3 3 3 5 a(i) + 34 b(i) + 34 c(i) = -10985 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 158, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 23 (202319022316610261861279311 t + 504840969387110277012949938 t - 1) ----------------------------------------------------------------------- 2 (t - 1) (t - 2291990322110298203822934274 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 2994880664477038826548340537 t + 272183140842538690183304894 t + 9 - ------------------------------------------------------------------- 2 (t - 1) (t - 2291990322110298203822934274 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 14 (169003662199305514417454593 t - 402365362579275337041143554 t + 1) ----------------------------------------------------------------------- 2 (t - 1) (t - 2291990322110298203822934274 t + 1) In Maple notation, these generating functions are 23*(202319022316610261861279311*t^2+504840969387110277012949938*t-1)/(t-1)/(t^2 -2291990322110298203822934274*t+1) -(2994880664477038826548340537*t^2+272183140842538690183304894*t+9)/(t-1)/(t^2-\ 2291990322110298203822934274*t+1) 14*(169003662199305514417454593*t^2-402365362579275337041143554*t+1)/(t-1)/(t^2 -2291990322110298203822934274*t+1) Then for all i>=0 we have 3 3 3 5 a(i) + 37 b(i) + 37 c(i) = -13720 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 159, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 9 (16839493277 t + 76743156326 t - 3) ) a(i) t = -------------------------------------- / 2 ----- (t - 1) (t - 151163884802 t + 1) i = 0 infinity ----- 2 \ i 11 (8843796241 t + 6138539758 t + 1) ) b(i) t = - ------------------------------------- / 2 ----- (t - 1) (t - 151163884802 t + 1) i = 0 infinity ----- 2 \ i 16 (4833765841 t - 15134121842 t + 1) ) c(i) t = -------------------------------------- / 2 ----- (t - 1) (t - 151163884802 t + 1) i = 0 In Maple notation, these generating functions are 9*(16839493277*t^2+76743156326*t-3)/(t-1)/(t^2-151163884802*t+1) -11*(8843796241*t^2+6138539758*t+1)/(t-1)/(t^2-151163884802*t+1) 16*(4833765841*t^2-15134121842*t+1)/(t-1)/(t^2-151163884802*t+1) Then for all i>=0 we have 3 3 3 5 a(i) + 38 b(i) + 38 c(i) = -6655 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 160, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 464390899 t + 2063991082 t - 29 ) a(i) t = -------------------------------- / 2 ----- (t - 1) (t - 416731394 t + 1) i = 0 infinity ----- 2 \ i 12 (24661153 t + 13596766 t + 1) ) b(i) t = - --------------------------------- / 2 ----- (t - 1) (t - 416731394 t + 1) i = 0 infinity ----- 2 \ i 239300801 t - 698395858 t + 17 ) c(i) t = ------------------------------- / 2 ----- (t - 1) (t - 416731394 t + 1) i = 0 In Maple notation, these generating functions are (464390899*t^2+2063991082*t-29)/(t-1)/(t^2-416731394*t+1) -12*(24661153*t^2+13596766*t+1)/(t-1)/(t^2-416731394*t+1) (239300801*t^2-698395858*t+17)/(t-1)/(t^2-416731394*t+1) Then for all i>=0 we have 3 3 3 5 a(i) + 41 b(i) + 41 c(i) = -8640 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 161, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 21277725612764100013 t + 55083310803042389614 t - 27 ) a(i) t = ----------------------------------------------------- / 2 ----- (t - 1) (t - 9448986023047771202 t + 1) i = 0 infinity ----- 2 \ i 11 (1227363427216355881 t - 24695283534691882 t + 1) ) b(i) t = - ----------------------------------------------------- / 2 ----- (t - 1) (t - 9448986023047771202 t + 1) i = 0 infinity ----- 2 \ i 16 (689177722397552081 t - 1516012071178696082 t + 1) ) c(i) t = ------------------------------------------------------ / 2 ----- (t - 1) (t - 9448986023047771202 t + 1) i = 0 In Maple notation, these generating functions are (21277725612764100013*t^2+55083310803042389614*t-27)/(t-1)/(t^2-\ 9448986023047771202*t+1) -11*(1227363427216355881*t^2-24695283534691882*t+1)/(t-1)/(t^2-\ 9448986023047771202*t+1) 16*(689177722397552081*t^2-1516012071178696082*t+1)/(t-1)/(t^2-\ 9448986023047771202*t+1) Then for all i>=0 we have 3 3 3 5 a(i) + 43 b(i) + 43 c(i) = -20480 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 162, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 1166169963450654937331 t + 3064667375599219371498 t - 29 ) a(i) t = --------------------------------------------------------- / 2 ----- (t - 1) (t - 493360918407631572802 t + 1) i = 0 infinity ----- 2 \ i 4 (183918066953198029283 t - 12478217062170705286 t + 3) ) b(i) t = - --------------------------------------------------------- / 2 ----- (t - 1) (t - 493360918407631572802 t + 1) i = 0 infinity ----- 2 \ i 17 (35818509593523225961 t - 76157297803176713962 t + 1) ) c(i) t = --------------------------------------------------------- / 2 ----- (t - 1) (t - 493360918407631572802 t + 1) i = 0 In Maple notation, these generating functions are (1166169963450654937331*t^2+3064667375599219371498*t-29)/(t-1)/(t^2-\ 493360918407631572802*t+1) -4*(183918066953198029283*t^2-12478217062170705286*t+3)/(t-1)/(t^2-\ 493360918407631572802*t+1) 17*(35818509593523225961*t^2-76157297803176713962*t+1)/(t-1)/(t^2-\ 493360918407631572802*t+1) Then for all i>=0 we have 3 3 3 5 a(i) + 46 b(i) + 46 c(i) = -24565 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 163, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 8 (11567356400695612613585926 t + 12794415472533402949294453 t - 3) -------------------------------------------------------------------- 2 (t - 1) (t - 16804280067327861599548994 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 58273974540081386832244747 t - 27348835362721123997528278 t + 11 - ----------------------------------------------------------------- 2 (t - 1) (t - 16804280067327861599548994 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 8 (6053676987648937969606559 t - 9919319384818970823946121 t + 2) ------------------------------------------------------------------ 2 (t - 1) (t - 16804280067327861599548994 t + 1) In Maple notation, these generating functions are 8*(11567356400695612613585926*t^2+12794415472533402949294453*t-3)/(t-1)/(t^2-\ 16804280067327861599548994*t+1) -(58273974540081386832244747*t^2-27348835362721123997528278*t+11)/(t-1)/(t^2-\ 16804280067327861599548994*t+1) 8*(6053676987648937969606559*t^2-9919319384818970823946121*t+2)/(t-1)/(t^2-\ 16804280067327861599548994*t+1) Then for all i>=0 we have 3 3 3 5 a(i) + 47 b(i) + 47 c(i) = -60835 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 164, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 28 ( / ----- i = 0 2 9070616058960723135951292238928798660714903858442771750325932843799 t + 15765322887550130144846331949187334811544100578496803864589696436202 t / 2 - 1) / ((t - 1) (t / - 65714649311132508411507614694555470625169257234015384245639614080002 t + 1)) infinity ----- \ i ) b(i) t = - 12 ( / ----- i = 0 2 13283406840341321376066064888679944530305504010576523358786138031001 t - 4459368039167483924943644030461761620646462657903771716030740431002 t / 2 + 1) / ((t - 1) (t / - 65714649311132508411507614694555470625169257234015384245639614080002 t + 1)) infinity ----- \ i ) c(i) t = ( / ----- i = 0 2 133484836201350933267217657981505623904480608531367503875930991104017 t - 239373301815436982680686708280123818820389104763440523588995762304034 t / 2 + 17) / ((t - 1) (t / - 65714649311132508411507614694555470625169257234015384245639614080002 t + 1)) In Maple notation, these generating functions are 28*(9070616058960723135951292238928798660714903858442771750325932843799*t^2+ 15765322887550130144846331949187334811544100578496803864589696436202*t-1)/(t-1) /(t^2-65714649311132508411507614694555470625169257234015384245639614080002*t+1) -12*(13283406840341321376066064888679944530305504010576523358786138031001*t^2-\ 4459368039167483924943644030461761620646462657903771716030740431002*t+1)/(t-1)/ (t^2-65714649311132508411507614694555470625169257234015384245639614080002*t+1) (133484836201350933267217657981505623904480608531367503875930991104017*t^2-\ 239373301815436982680686708280123818820389104763440523588995762304034*t+17)/(t-\ 1)/(t^2-65714649311132508411507614694555470625169257234015384245639614080002*t+ 1) Then for all i>=0 we have 3 3 3 5 a(i) + 49 b(i) + 49 c(i) = -46305 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 165, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 8 (4700687326358293 t + 376640010376924174 t - 3) ) a(i) t = -------------------------------------------------- / 2 ----- (t - 1) (t - 2005956546822746114 t + 1) i = 0 infinity ----- 2 \ i 17252539615625273 t + 1340947205628942406 t + 1 ) b(i) t = - ------------------------------------------------ / 2 ----- (t - 1) (t - 2005956546822746114 t + 1) i = 0 infinity ----- 2 \ i 2788886303753603 t - 1360988631548321294 t + 11 ) c(i) t = ------------------------------------------------ / 2 ----- (t - 1) (t - 2005956546822746114 t + 1) i = 0 In Maple notation, these generating functions are 8*(4700687326358293*t^2+376640010376924174*t-3)/(t-1)/(t^2-2005956546822746114* t+1) -(17252539615625273*t^2+1340947205628942406*t+1)/(t-1)/(t^2-2005956546822746114 *t+1) (2788886303753603*t^2-1360988631548321294*t+11)/(t-1)/(t^2-2005956546822746114* t+1) Then for all i>=0 we have 3 3 3 5 a(i) + 52 b(i) + 52 c(i) = -40 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 166, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 27 (133844031606834671884553182605710106239 t / ----- i = 0 / + 245688469472189134894274866091093664962 t - 1) / ((t - 1) / 2 (t - 907788432349428849893174510729705428802 t + 1)) infinity ----- \ i 2 ) b(i) t = - 4 (437575013313818489718207482890315683361 t / ----- i = 0 / + 325730575448464026708485799404932124638 t + 1) / ((t - 1) / 2 (t - 907788432349428849893174510729705428802 t + 1)) infinity ----- \ i 2 ) c(i) t = 14 (71244812533344923537301305671724527561 t / ----- i = 0 / - 289332123608282785373499386327509615562 t + 1) / ((t - 1) / 2 (t - 907788432349428849893174510729705428802 t + 1)) In Maple notation, these generating functions are 27*(133844031606834671884553182605710106239*t^2+ 245688469472189134894274866091093664962*t-1)/(t-1)/(t^2-\ 907788432349428849893174510729705428802*t+1) -4*(437575013313818489718207482890315683361*t^2+ 325730575448464026708485799404932124638*t+1)/(t-1)/(t^2-\ 907788432349428849893174510729705428802*t+1) 14*(71244812533344923537301305671724527561*t^2-\ 289332123608282785373499386327509615562*t+1)/(t-1)/(t^2-\ 907788432349428849893174510729705428802*t+1) Then for all i>=0 we have 3 3 3 5 a(i) + 54 b(i) + 54 c(i) = -46305 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 167, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 2 (10400318695606109446367759715640075481696531989 t / ----- i = 0 / + 204127998991732626391461038608233919623588127222 t - 11) / ((t - 1) / 2 (t - 266074023310154679231357456960045092327378227202 t + 1)) infinity ----- \ i 2 ) b(i) t = - 5 (1934765206983839058236946310427822300047948801 t / ----- i = 0 / + 22610808899118991129157653040129843043806131198 t + 1) / ((t - 1) / 2 (t - 266074023310154679231357456960045092327378227202 t + 1)) infinity ----- \ i 2 ) c(i) t = 10 (551369855667675151263762766588308130756113121 t / ----- i = 0 / - 12824156908719090244961062441867140802683153122 t + 1) / ((t - 1) / 2 (t - 266074023310154679231357456960045092327378227202 t + 1)) In Maple notation, these generating functions are 2*(10400318695606109446367759715640075481696531989*t^2+ 204127998991732626391461038608233919623588127222*t-11)/(t-1)/(t^2-\ 266074023310154679231357456960045092327378227202*t+1) -5*(1934765206983839058236946310427822300047948801*t^2+ 22610808899118991129157653040129843043806131198*t+1)/(t-1)/(t^2-\ 266074023310154679231357456960045092327378227202*t+1) 10*(551369855667675151263762766588308130756113121*t^2-\ 12824156908719090244961062441867140802683153122*t+1)/(t-1)/(t^2-\ 266074023310154679231357456960045092327378227202*t+1) Then for all i>=0 we have 3 3 3 5 a(i) + 61 b(i) + 61 c(i) = -135 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 168, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 20 ( / ----- i = 0 2 14891804921947687989080335620007366490077090581168910250729865145823 t + 74882081699299762382168779390917820010974649527898798994382255512098 t / 2 - 1) / ((t - 1) (t / - 425194884946625582454544859070732159693799908322483137669360149529602 t + 1)) infinity ----- \ i ) b(i) t = - 4 ( / ----- i = 0 2 34822385135297440617367047444647304139830994823440579419510407896081 t + 81182900846799739450966460876432182636317087068550922505871815527918 t / 2 + 1) / ((t - 1) (t / - 425194884946625582454544859070732159693799908322483137669360149529602 t + 1)) infinity ----- \ i ) c(i) t = 9 ( / ----- i = 0 2 9567169218089462500940776792856196089894295087731959801238806229281 t - 61125074099021542531311224935558190212626775928617071768075349973282 t / 2 + 1) / ((t - 1) (t / - 425194884946625582454544859070732159693799908322483137669360149529602 t + 1)) In Maple notation, these generating functions are 20*(14891804921947687989080335620007366490077090581168910250729865145823*t^2+ 74882081699299762382168779390917820010974649527898798994382255512098*t-1)/(t-1) /(t^2-425194884946625582454544859070732159693799908322483137669360149529602*t+1 ) -4*(34822385135297440617367047444647304139830994823440579419510407896081*t^2+ 81182900846799739450966460876432182636317087068550922505871815527918*t+1)/(t-1) /(t^2-425194884946625582454544859070732159693799908322483137669360149529602*t+1 ) 9*(9567169218089462500940776792856196089894295087731959801238806229281*t^2-\ 61125074099021542531311224935558190212626775928617071768075349973282*t+1)/(t-1) /(t^2-425194884946625582454544859070732159693799908322483137669360149529602*t+1 ) Then for all i>=0 we have 3 3 3 5 a(i) + 64 b(i) + 64 c(i) = -2560 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 169, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 2 (74424371570102828703667789577630729303123 t / ----- i = 0 / + 791580935605130175384167352976716764204474 t - 13) / ((t - 1) / 2 (t - 337205606333719045839511028959214953224194 t + 1)) infinity ----- \ i 2 ) b(i) t = - (62957902853249668222603192117054626728833 t / ----- i = 0 / + 588462018473253033967361295645065169272446 t + 1) / ((t - 1) / 2 (t - 337205606333719045839511028959214953224194 t + 1)) infinity ----- \ i 2 ) c(i) t = (19178860753189180749857433541977727138763 t / ----- i = 0 / - 670598782079691882939821921304097523140054 t + 11) / ((t - 1) / 2 (t - 337205606333719045839511028959214953224194 t + 1)) In Maple notation, these generating functions are 2*(74424371570102828703667789577630729303123*t^2+ 791580935605130175384167352976716764204474*t-13)/(t-1)/(t^2-\ 337205606333719045839511028959214953224194*t+1) -(62957902853249668222603192117054626728833*t^2+ 588462018473253033967361295645065169272446*t+1)/(t-1)/(t^2-\ 337205606333719045839511028959214953224194*t+1) (19178860753189180749857433541977727138763*t^2-\ 670598782079691882939821921304097523140054*t+11)/(t-1)/(t^2-\ 337205606333719045839511028959214953224194*t+1) Then for all i>=0 we have 3 3 3 5 a(i) + 68 b(i) + 68 c(i) = -2560 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 170, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (533323856952370004014452230636135977702784995 t / ----- i = 0 / + 1370635039654916423683408940326458317259276346 t - 29) / ((t - 1) / 2 (t - 182041109275410348189359265220075609465552898 t + 1)) infinity ----- \ i 2 ) b(i) t = - 3 (76803927327422028984600250994693672649612289 t / ----- i = 0 / + 109402321729525298907611110468640732725650430 t + 1) / ((t - 1) / 2 (t - 182041109275410348189359265220075609465552898 t + 1)) infinity ----- \ i 2 ) c(i) t = (119302645117189002784123204934886022594089997 t / ----- i = 0 / - 677921392288030986460757289324889238719878170 t + 13) / ((t - 1) / 2 (t - 182041109275410348189359265220075609465552898 t + 1)) In Maple notation, these generating functions are (533323856952370004014452230636135977702784995*t^2+ 1370635039654916423683408940326458317259276346*t-29)/(t-1)/(t^2-\ 182041109275410348189359265220075609465552898*t+1) -3*(76803927327422028984600250994693672649612289*t^2+ 109402321729525298907611110468640732725650430*t+1)/(t-1)/(t^2-\ 182041109275410348189359265220075609465552898*t+1) (119302645117189002784123204934886022594089997*t^2-\ 677921392288030986460757289324889238719878170*t+13)/(t-1)/(t^2-\ 182041109275410348189359265220075609465552898*t+1) Then for all i>=0 we have 3 3 3 5 a(i) + 72 b(i) + 72 c(i) = -34295 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 171, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 6739800545588442244432550437 t + 1600023732194222336230868470966 t - 27 ------------------------------------------------------------------------ 2 (t - 1) (t - 1998272553799879144775905849154 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 2746844347035741236522240713 t + 641009599677908887915478986166 t + 1 - ---------------------------------------------------------------------- 2 (t - 1) (t - 1998272553799879144775905849154 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 339772723611297577796329843 t - 644096216748555926729797556734 t + 11 ---------------------------------------------------------------------- 2 (t - 1) (t - 1998272553799879144775905849154 t + 1) In Maple notation, these generating functions are (6739800545588442244432550437*t^2+1600023732194222336230868470966*t-27)/(t-1)/( t^2-1998272553799879144775905849154*t+1) -(2746844347035741236522240713*t^2+641009599677908887915478986166*t+1)/(t-1)/(t ^2-1998272553799879144775905849154*t+1) (339772723611297577796329843*t^2-644096216748555926729797556734*t+11)/(t-1)/(t^ 2-1998272553799879144775905849154*t+1) Then for all i>=0 we have 3 3 3 5 a(i) + 74 b(i) + 74 c(i) = -5 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 172, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 9 (6378340833753612334484632371359592412041108935677 t / ----- i = 0 / + 42284925366567369046218843018615144964902460369926 t - 3) / ((t - 1) / 2 (t - 64598221479972845810852671325010694375542320332802 t + 1)) infinity ----- \ i 2 ) b(i) t = - (23211078503419603237908662279164075788672937904641 t / ----- i = 0 / + 127913899402184362070737477600426749806518857807358 t + 1) / ((t - 1) / 2 (t - 64598221479972845810852671325010694375542320332802 t + 1)) infinity ----- \ i 2 ) c(i) t = 11 (736771071990717255829933620061893691114525923841 t / ----- i = 0 / - 14475405427045623192979582700024696017950143715842 t + 1) / ((t - 1) / 2 (t - 64598221479972845810852671325010694375542320332802 t + 1)) In Maple notation, these generating functions are 9*(6378340833753612334484632371359592412041108935677*t^2+ 42284925366567369046218843018615144964902460369926*t-3)/(t-1)/(t^2-\ 64598221479972845810852671325010694375542320332802*t+1) -(23211078503419603237908662279164075788672937904641*t^2+ 127913899402184362070737477600426749806518857807358*t+1)/(t-1)/(t^2-\ 64598221479972845810852671325010694375542320332802*t+1) 11*(736771071990717255829933620061893691114525923841*t^2-\ 14475405427045623192979582700024696017950143715842*t+1)/(t-1)/(t^2-\ 64598221479972845810852671325010694375542320332802*t+1) Then for all i>=0 we have 3 3 3 5 a(i) + 79 b(i) + 79 c(i) = -6655 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 173, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 2 (27001497463482672930449136200792965524914466442584841 t / ----- i = 0 / + 294129043530749570671187638603862554040449108293152290 t - 11) / ( / 2 (t - 1) (t - 238051367766370203280430548524468710002660904324652098 t + 1) ) infinity ----- \ i 2 ) b(i) t = - 4 (5692068330847564664873661414909184497047768232412079 t / ----- i = 0 / + 36727327984437516437103799053416153214619631561447520 t + 1) / ( / 2 (t - 1) (t - 238051367766370203280430548524468710002660904324652098 t + 1) ) infinity ----- \ i 2 ) c(i) t = (12767718707285564981550521140824528534519048321283561 t / ----- i = 0 / - 182445303968425889389460363014125879381188647496721970 t + 9) / ( / 2 (t - 1) (t - 238051367766370203280430548524468710002660904324652098 t + 1) ) In Maple notation, these generating functions are 2*(27001497463482672930449136200792965524914466442584841*t^2+ 294129043530749570671187638603862554040449108293152290*t-11)/(t-1)/(t^2-\ 238051367766370203280430548524468710002660904324652098*t+1) -4*(5692068330847564664873661414909184497047768232412079*t^2+ 36727327984437516437103799053416153214619631561447520*t+1)/(t-1)/(t^2-\ 238051367766370203280430548524468710002660904324652098*t+1) (12767718707285564981550521140824528534519048321283561*t^2-\ 182445303968425889389460363014125879381188647496721970*t+9)/(t-1)/(t^2-\ 238051367766370203280430548524468710002660904324652098*t+1) Then for all i>=0 we have 3 3 3 5 a(i) + 81 b(i) + 81 c(i) = -625 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 174, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (27553139 t + 71693978 t - 13) ) a(i) t = --------------------------------- / 2 ----- (t - 1) (t - 18957314 t + 1) i = 0 infinity ----- 2 \ i 21753601 t + 39578878 t + 1 ) b(i) t = - ----------------------------- / 2 ----- (t - 1) (t - 18957314 t + 1) i = 0 infinity ----- 2 \ i 11 (839041 t - 6414722 t + 1) ) c(i) t = ------------------------------ / 2 ----- (t - 1) (t - 18957314 t + 1) i = 0 In Maple notation, these generating functions are 2*(27553139*t^2+71693978*t-13)/(t-1)/(t^2-18957314*t+1) -(21753601*t^2+39578878*t+1)/(t-1)/(t^2-18957314*t+1) 11*(839041*t^2-6414722*t+1)/(t-1)/(t^2-18957314*t+1) Then for all i>=0 we have 3 3 3 5 a(i) + 88 b(i) + 88 c(i) = -29160 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 175, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 8 (26432262360400584821429 t + 40837864948768425914798 t - 3) -------------------------------------------------------------- 2 (t - 1) (t - 42586458362469689321474 t + 1) infinity ----- 2 \ i 82567406723841302372201 t + 77765539194385355341078 t + 1 ) b(i) t = - ---------------------------------------------------------- / 2 ----- (t - 1) (t - 42586458362469689321474 t + 1) i = 0 infinity ----- \ i ) c(i) t = / ----- i = 0 2 11 (3327114072064531864441 t - 17902836428266955292922 t + 1) -------------------------------------------------------------- 2 (t - 1) (t - 42586458362469689321474 t + 1) In Maple notation, these generating functions are 8*(26432262360400584821429*t^2+40837864948768425914798*t-3)/(t-1)/(t^2-\ 42586458362469689321474*t+1) -(82567406723841302372201*t^2+77765539194385355341078*t+1)/(t-1)/(t^2-\ 42586458362469689321474*t+1) 11*(3327114072064531864441*t^2-17902836428266955292922*t+1)/(t-1)/(t^2-\ 42586458362469689321474*t+1) Then for all i>=0 we have 3 3 3 5 a(i) + 92 b(i) + 92 c(i) = -53240 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 176, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 4 (1860431118116222812783187 t + 25813915879824240841389380 t - 7) ------------------------------------------------------------------- 2 (t - 1) (t - 42067955436549711461522498 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 6 (503815716513040577864349 t + 3549683843771181794917250 t + 1) - ----------------------------------------------------------------- 2 (t - 1) (t - 42067955436549711461522498 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 1895360288098714489741739 t - 26216357649804048726431350 t + 11 ---------------------------------------------------------------- 2 (t - 1) (t - 42067955436549711461522498 t + 1) In Maple notation, these generating functions are 4*(1860431118116222812783187*t^2+25813915879824240841389380*t-7)/(t-1)/(t^2-\ 42067955436549711461522498*t+1) -6*(503815716513040577864349*t^2+3549683843771181794917250*t+1)/(t-1)/(t^2-\ 42067955436549711461522498*t+1) (1895360288098714489741739*t^2-26216357649804048726431350*t+11)/(t-1)/(t^2-\ 42067955436549711461522498*t+1) Then for all i>=0 we have 3 3 3 5 a(i) + 99 b(i) + 99 c(i) = -625 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 177, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 5334196820000028596271089251 t + 14001923344447428659636830906 t - 29 ---------------------------------------------------------------------- 2 (t - 1) (t - 1827890766695339597518122242 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 6 (881939254718976972186067345 t + 1370812609100144261511942766 t + 1) - ----------------------------------------------------------------------- 2 (t - 1) (t - 1827890766695339597518122242 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 6 (437422853052307922496809909 t - 2690174716871429156194820026 t + 5) ----------------------------------------------------------------------- 2 (t - 1) (t - 1827890766695339597518122242 t + 1) In Maple notation, these generating functions are (5334196820000028596271089251*t^2+14001923344447428659636830906*t-29)/(t-1)/(t^ 2-1827890766695339597518122242*t+1) -6*(881939254718976972186067345*t^2+1370812609100144261511942766*t+1)/(t-1)/(t^ 2-1827890766695339597518122242*t+1) 6*(437422853052307922496809909*t^2-2690174716871429156194820026*t+5)/(t-1)/(t^2 -1827890766695339597518122242*t+1) Then for all i>=0 we have 3 3 3 6 a(i) + 7 b(i) + 7 c(i) = -41154 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 178, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 4 (5613788 t + 107914469 t - 7) ) a(i) t = -------------------------------- / 2 ----- (t - 1) (t - 146361602 t + 1) i = 0 infinity ----- 2 \ i 5 (3719431 t + 60967168 t + 1) ) b(i) t = - ------------------------------- / 2 ----- (t - 1) (t - 146361602 t + 1) i = 0 infinity ----- 2 \ i 6348893 t - 329781916 t + 23 ) c(i) t = ------------------------------ / 2 ----- (t - 1) (t - 146361602 t + 1) i = 0 In Maple notation, these generating functions are 4*(5613788*t^2+107914469*t-7)/(t-1)/(t^2-146361602*t+1) -5*(3719431*t^2+60967168*t+1)/(t-1)/(t^2-146361602*t+1) (6348893*t^2-329781916*t+23)/(t-1)/(t^2-146361602*t+1) Then for all i>=0 we have 3 3 3 6 a(i) + 11 b(i) + 11 c(i) = -750 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 179, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 3201860023158792078697 t + 274425465404719245314926 t - 23 ) a(i) t = ----------------------------------------------------------- / 2 ----- (t - 1) (t - 455920103225597877921602 t + 1) i = 0 infinity ----- \ i ) b(i) t = / ----- i = 0 2 6 (419226028165163754361 t + 30145250165729666050438 t + 1) - ------------------------------------------------------------ 2 (t - 1) (t - 455920103225597877921602 t + 1) infinity ----- 2 \ i 18 (50801453189532582601 t - 10238960184487809184202 t + 1) ) c(i) t = ------------------------------------------------------------ / 2 ----- (t - 1) (t - 455920103225597877921602 t + 1) i = 0 In Maple notation, these generating functions are (3201860023158792078697*t^2+274425465404719245314926*t-23)/(t-1)/(t^2-\ 455920103225597877921602*t+1) -6*(419226028165163754361*t^2+30145250165729666050438*t+1)/(t-1)/(t^2-\ 455920103225597877921602*t+1) 18*(50801453189532582601*t^2-10238960184487809184202*t+1)/(t-1)/(t^2-\ 455920103225597877921602*t+1) Then for all i>=0 we have 3 3 3 6 a(i) + 13 b(i) + 13 c(i) = -6 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 180, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 4 (13061042 t + 22568771 t - 7) ) a(i) t = -------------------------------- / 2 ----- (t - 1) (t - 11303042 t + 1) i = 0 infinity ----- 2 \ i 38909363 t + 32118128 t + 5 ) b(i) t = - ----------------------------- / 2 ----- (t - 1) (t - 11303042 t + 1) i = 0 infinity ----- 2 \ i 23 (890011 t - 3978164 t + 1) ) c(i) t = ------------------------------ / 2 ----- (t - 1) (t - 11303042 t + 1) i = 0 In Maple notation, these generating functions are 4*(13061042*t^2+22568771*t-7)/(t-1)/(t^2-11303042*t+1) -(38909363*t^2+32118128*t+5)/(t-1)/(t^2-11303042*t+1) 23*(890011*t^2-3978164*t+1)/(t-1)/(t^2-11303042*t+1) Then for all i>=0 we have 3 3 3 6 a(i) + 17 b(i) + 17 c(i) = -73002 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 181, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 17 (63916368080238662357282759 t + 80448700098021148080928442 t - 1) --------------------------------------------------------------------- 2 (t - 1) (t - 289687464394836993624686402 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 3 (168496247432668003541343001 t + 46328164365750441169098598 t + 1) - --------------------------------------------------------------------- 2 (t - 1) (t - 289687464394836993624686402 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 9 (34214339904544743401178841 t - 105822477170684224971326042 t + 1) --------------------------------------------------------------------- 2 (t - 1) (t - 289687464394836993624686402 t + 1) In Maple notation, these generating functions are 17*(63916368080238662357282759*t^2+80448700098021148080928442*t-1)/(t-1)/(t^2-\ 289687464394836993624686402*t+1) -3*(168496247432668003541343001*t^2+46328164365750441169098598*t+1)/(t-1)/(t^2-\ 289687464394836993624686402*t+1) 9*(34214339904544743401178841*t^2-105822477170684224971326042*t+1)/(t-1)/(t^2-\ 289687464394836993624686402*t+1) Then for all i>=0 we have 3 3 3 6 a(i) + 77 b(i) + 77 c(i) = -24576 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 182, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 165467423 t + 14332075898 t - 25 ) a(i) t = --------------------------------- / 2 ----- (t - 1) (t - 9447451202 t + 1) i = 0 infinity ----- 2 \ i 2 (76180609 t + 6416794942 t + 1) ) b(i) t = - ---------------------------------- / 2 ----- (t - 1) (t - 9447451202 t + 1) i = 0 infinity ----- 2 \ i 23664335 t - 13009615462 t + 23 ) c(i) t = -------------------------------- / 2 ----- (t - 1) (t - 9447451202 t + 1) i = 0 In Maple notation, these generating functions are (165467423*t^2+14332075898*t-25)/(t-1)/(t^2-9447451202*t+1) -2*(76180609*t^2+6416794942*t+1)/(t-1)/(t^2-9447451202*t+1) (23664335*t^2-13009615462*t+23)/(t-1)/(t^2-9447451202*t+1) Then for all i>=0 we have 3 3 3 7 a(i) + 9 b(i) + 9 c(i) = -56 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 183, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (28464911505785507385181781231983 t / ----- i = 0 / + 47226693686293492534969133328034 t - 17) / ((t - 1) / 2 (t - 11632394604547802161999802880002 t + 1)) infinity ----- \ i ) b(i) t = - 22 ( / ----- i = 0 2 2040743226480489205325479483201 t - 1525032465000488232538778683202 t + 1) / 2 / ((t - 1) (t - 11632394604547802161999802880002 t + 1)) / infinity ----- \ i ) c(i) t = 25 ( / ----- i = 0 2 1681994393279688471145694820289 t - 2135819863382089327197991524290 t + 1) / 2 / ((t - 1) (t - 11632394604547802161999802880002 t + 1)) / In Maple notation, these generating functions are (28464911505785507385181781231983*t^2+47226693686293492534969133328034*t-17)/(t -1)/(t^2-11632394604547802161999802880002*t+1) -22*(2040743226480489205325479483201*t^2-1525032465000488232538778683202*t+1)/( t-1)/(t^2-11632394604547802161999802880002*t+1) 25*(1681994393279688471145694820289*t^2-2135819863382089327197991524290*t+1)/(t -1)/(t^2-11632394604547802161999802880002*t+1) Then for all i>=0 we have 3 3 3 7 a(i) + 10 b(i) + 10 c(i) = -15379 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 184, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 27955 t + 866026 t - 29 ) a(i) t = --------------------------- / 2 ----- (t - 1) (t - 334082 t + 1) i = 0 infinity ----- 2 \ i 4 (6049 t + 171358 t + 1) ) b(i) t = - --------------------------- / 2 ----- (t - 1) (t - 334082 t + 1) i = 0 infinity ----- 2 \ i 6409 t - 716066 t + 25 ) c(i) t = --------------------------- / 2 ----- (t - 1) (t - 334082 t + 1) i = 0 In Maple notation, these generating functions are (27955*t^2+866026*t-29)/(t-1)/(t^2-334082*t+1) -4*(6049*t^2+171358*t+1)/(t-1)/(t^2-334082*t+1) (6409*t^2-716066*t+25)/(t-1)/(t^2-334082*t+1) Then for all i>=0 we have 3 3 3 7 a(i) + 11 b(i) + 11 c(i) = -448 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 185, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 9 (198544211618985649304053 t + 805115615684145824958734 t - 3) ---------------------------------------------------------------- 2 (t - 1) (t - 1480010286500595566153282 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 16 (111098376347172336501271 t + 82120819929765139908856 t + 1) - ---------------------------------------------------------------- 2 (t - 1) (t - 1480010286500595566153282 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 1365212966653787189311921 t - 4456720107084786811873994 t + 25 --------------------------------------------------------------- 2 (t - 1) (t - 1480010286500595566153282 t + 1) In Maple notation, these generating functions are 9*(198544211618985649304053*t^2+805115615684145824958734*t-3)/(t-1)/(t^2-\ 1480010286500595566153282*t+1) -16*(111098376347172336501271*t^2+82120819929765139908856*t+1)/(t-1)/(t^2-\ 1480010286500595566153282*t+1) (1365212966653787189311921*t^2-4456720107084786811873994*t+25)/(t-1)/(t^2-\ 1480010286500595566153282*t+1) Then for all i>=0 we have 3 3 3 7 a(i) + 13 b(i) + 13 c(i) = -12096 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 186, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 892525758692697697 t + 1325029655741133622 t - 23 ) a(i) t = -------------------------------------------------- / 2 ----- (t - 1) (t - 171901954607687234 t + 1) i = 0 infinity ----- 2 \ i 709332073808498617 t + 690527556545523142 t + 1 ) b(i) t = - ------------------------------------------------ / 2 ----- (t - 1) (t - 171901954607687234 t + 1) i = 0 infinity ----- 2 \ i 22 (13310002412965441 t - 76939985610875522 t + 1) ) c(i) t = --------------------------------------------------- / 2 ----- (t - 1) (t - 171901954607687234 t + 1) i = 0 In Maple notation, these generating functions are (892525758692697697*t^2+1325029655741133622*t-23)/(t-1)/(t^2-171901954607687234 *t+1) -(709332073808498617*t^2+690527556545523142*t+1)/(t-1)/(t^2-171901954607687234* t+1) 22*(13310002412965441*t^2-76939985610875522*t+1)/(t-1)/(t^2-171901954607687234* t+1) Then for all i>=0 we have 3 3 3 7 a(i) + 15 b(i) + 15 c(i) = -74536 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 187, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 5 (37712183199739 t + 249815813093386 t - 5) ) a(i) t = --------------------------------------------- / 2 ----- (t - 1) (t - 282025068134402 t + 1) i = 0 infinity ----- 2 \ i 5 (29070960743425 t + 134641151978494 t + 1) ) b(i) t = - --------------------------------------------- / 2 ----- (t - 1) (t - 282025068134402 t + 1) i = 0 infinity ----- 2 \ i 67712073600019 t - 886272637209638 t + 19 ) c(i) t = ------------------------------------------ / 2 ----- (t - 1) (t - 282025068134402 t + 1) i = 0 In Maple notation, these generating functions are 5*(37712183199739*t^2+249815813093386*t-5)/(t-1)/(t^2-282025068134402*t+1) -5*(29070960743425*t^2+134641151978494*t+1)/(t-1)/(t^2-282025068134402*t+1) (67712073600019*t^2-886272637209638*t+19)/(t-1)/(t^2-282025068134402*t+1) Then for all i>=0 we have 3 3 3 7 a(i) + 17 b(i) + 17 c(i) = -5103 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 188, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 29 (444305394719 t + 729665645282 t - 1) ) a(i) t = ----------------------------------------- / 2 ----- (t - 1) (t - 2436402566402 t + 1) i = 0 infinity ----- 2 \ i 4 (2450619605281 t + 2165259354718 t + 1) ) b(i) t = - ------------------------------------------ / 2 ----- (t - 1) (t - 2436402566402 t + 1) i = 0 infinity ----- 2 \ i 25 (191668036561 t - 930208670162 t + 1) ) c(i) t = ----------------------------------------- / 2 ----- (t - 1) (t - 2436402566402 t + 1) i = 0 In Maple notation, these generating functions are 29*(444305394719*t^2+729665645282*t-1)/(t-1)/(t^2-2436402566402*t+1) -4*(2450619605281*t^2+2165259354718*t+1)/(t-1)/(t^2-2436402566402*t+1) 25*(191668036561*t^2-930208670162*t+1)/(t-1)/(t^2-2436402566402*t+1) Then for all i>=0 we have 3 3 3 7 a(i) + 18 b(i) + 18 c(i) = -109375 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 189, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 13248696587223299493581 t + 751441041920298120069638 t - 19 ) a(i) t = ------------------------------------------------------------ / 2 ----- (t - 1) (t - 1396977366814093900756802 t + 1) i = 0 infinity ----- 2 \ i 9849622252794953322607 t + 368442121178487727733386 t + 7 ) b(i) t = - ---------------------------------------------------------- / 2 ----- (t - 1) (t - 1396977366814093900756802 t + 1) i = 0 infinity ----- \ i ) c(i) t = / ----- i = 0 2 2 (2606289223633399249927 t - 191752160939274739777934 t + 7) -------------------------------------------------------------- 2 (t - 1) (t - 1396977366814093900756802 t + 1) In Maple notation, these generating functions are (13248696587223299493581*t^2+751441041920298120069638*t-19)/(t-1)/(t^2-\ 1396977366814093900756802*t+1) -(9849622252794953322607*t^2+368442121178487727733386*t+7)/(t-1)/(t^2-\ 1396977366814093900756802*t+1) 2*(2606289223633399249927*t^2-191752160939274739777934*t+7)/(t-1)/(t^2-\ 1396977366814093900756802*t+1) Then for all i>=0 we have 3 3 3 7 a(i) + 20 b(i) + 20 c(i) = -7 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 190, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 18443192976986783 t + 145282815354813234 t - 17 ) a(i) t = ------------------------------------------------ / 2 ----- (t - 1) (t - 60757321085960002 t + 1) i = 0 infinity ----- 2 \ i 5 (2689342170442201 t + 12186059176517798 t + 1) ) b(i) t = - ------------------------------------------------- / 2 ----- (t - 1) (t - 60757321085960002 t + 1) i = 0 infinity ----- 2 \ i 4 (1894605544428803 t - 20488857228128806 t + 3) ) c(i) t = ------------------------------------------------- / 2 ----- (t - 1) (t - 60757321085960002 t + 1) i = 0 In Maple notation, these generating functions are (18443192976986783*t^2+145282815354813234*t-17)/(t-1)/(t^2-60757321085960002*t+ 1) -5*(2689342170442201*t^2+12186059176517798*t+1)/(t-1)/(t^2-60757321085960002*t+ 1) 4*(1894605544428803*t^2-20488857228128806*t+3)/(t-1)/(t^2-60757321085960002*t+1 ) Then for all i>=0 we have 3 3 3 7 a(i) + 22 b(i) + 22 c(i) = -875 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 191, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 102275 t + 299226 t - 29 ) a(i) t = -------------------------- / 2 ----- (t - 1) (t - 44098 t + 1) i = 0 infinity ----- 2 \ i 7 (10561 t + 14462 t + 1) ) b(i) t = - -------------------------- / 2 ----- (t - 1) (t - 44098 t + 1) i = 0 infinity ----- 2 \ i 7 (6115 t - 31142 t + 3) ) c(i) t = -------------------------- / 2 ----- (t - 1) (t - 44098 t + 1) i = 0 In Maple notation, these generating functions are (102275*t^2+299226*t-29)/(t-1)/(t^2-44098*t+1) -7*(10561*t^2+14462*t+1)/(t-1)/(t^2-44098*t+1) 7*(6115*t^2-31142*t+3)/(t-1)/(t^2-44098*t+1) Then for all i>=0 we have 3 3 3 7 a(i) + 23 b(i) + 23 c(i) = -34391 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 192, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 3 (759191 t + 1152946 t - 9) ) a(i) t = ----------------------------- / 2 ----- (t - 1) (t - 470594 t + 1) i = 0 infinity ----- 2 \ i 7 (231553 t + 99646 t + 1) ) b(i) t = - --------------------------- / 2 ----- (t - 1) (t - 470594 t + 1) i = 0 infinity ----- 2 \ i 21 (46817 t - 157218 t + 1) ) c(i) t = ---------------------------- / 2 ----- (t - 1) (t - 470594 t + 1) i = 0 In Maple notation, these generating functions are 3*(759191*t^2+1152946*t-9)/(t-1)/(t^2-470594*t+1) -7*(231553*t^2+99646*t+1)/(t-1)/(t^2-470594*t+1) 21*(46817*t^2-157218*t+1)/(t-1)/(t^2-470594*t+1) Then for all i>=0 we have 3 3 3 7 a(i) + 25 b(i) + 25 c(i) = -85169 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 193, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (106029008483186655623443718572912783 t / ----- i = 0 / + 321803188113192457620807199072879234 t - 17) / ((t - 1) / 2 (t - 95058754299227181738263040656006402 t + 1)) infinity ----- \ i 2 ) b(i) t = - 2 (81998363356106068095842075032302491 t / ----- i = 0 / - 69658353882169301279605360767400102 t + 11) / ((t - 1) / 2 (t - 95058754299227181738263040656006402 t + 1)) infinity ----- \ i 2 ) c(i) t = (159918687924397264821551699350262183 t / ----- i = 0 / - 184598706872270798454025127880067006 t + 23) / ((t - 1) / 2 (t - 95058754299227181738263040656006402 t + 1)) In Maple notation, these generating functions are (106029008483186655623443718572912783*t^2+321803188113192457620807199072879234* t-17)/(t-1)/(t^2-95058754299227181738263040656006402*t+1) -2*(81998363356106068095842075032302491*t^2-69658353882169301279605360767400102 *t+11)/(t-1)/(t^2-95058754299227181738263040656006402*t+1) (159918687924397264821551699350262183*t^2-184598706872270798454025127880067006* t+23)/(t-1)/(t^2-95058754299227181738263040656006402*t+1) Then for all i>=0 we have 3 3 3 7 a(i) + 26 b(i) + 26 c(i) = -5103 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 194, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 24 (92411547838236379 t + 1053998868995818662 t - 1) ) a(i) t = ----------------------------------------------------- / 2 ----- (t - 1) (t - 10538233710377518082 t + 1) i = 0 infinity ----- 2 \ i 3 (512935589573765123 t + 2713703087962639354 t + 3) ) b(i) t = - ----------------------------------------------------- / 2 ----- (t - 1) (t - 10538233710377518082 t + 1) i = 0 infinity ----- 2 \ i 16 (62716069517443651 t - 667710821555519492 t + 1) ) c(i) t = ---------------------------------------------------- / 2 ----- (t - 1) (t - 10538233710377518082 t + 1) i = 0 In Maple notation, these generating functions are 24*(92411547838236379*t^2+1053998868995818662*t-1)/(t-1)/(t^2-\ 10538233710377518082*t+1) -3*(512935589573765123*t^2+2713703087962639354*t+3)/(t-1)/(t^2-\ 10538233710377518082*t+1) 16*(62716069517443651*t^2-667710821555519492*t+1)/(t-1)/(t^2-\ 10538233710377518082*t+1) Then for all i>=0 we have 3 3 3 7 a(i) + 29 b(i) + 29 c(i) = -875 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 195, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 20 (455401492178742883561246540496531711 t / ----- i = 0 / + 716255885336463305451236611082727170 t - 1) / ((t - 1) / 2 (t - 2883135955142130412753230791844249602 t + 1)) infinity ----- \ i 2 ) b(i) t = - 3 (2255813090128159199857132700677328003 t / ----- i = 0 / - 323498567000986689182095042313628806 t + 3) / ((t - 1) / 2 (t - 2883135955142130412753230791844249602 t + 1)) infinity ----- \ i 2 ) c(i) t = 15 (349962286430355643624482864469569665 t / ----- i = 0 / - 736425191055790145759490396142309506 t + 1) / ((t - 1) / 2 (t - 2883135955142130412753230791844249602 t + 1)) In Maple notation, these generating functions are 20*(455401492178742883561246540496531711*t^2+ 716255885336463305451236611082727170*t-1)/(t-1)/(t^2-\ 2883135955142130412753230791844249602*t+1) -3*(2255813090128159199857132700677328003*t^2-\ 323498567000986689182095042313628806*t+3)/(t-1)/(t^2-\ 2883135955142130412753230791844249602*t+1) 15*(349962286430355643624482864469569665*t^2-\ 736425191055790145759490396142309506*t+1)/(t-1)/(t^2-\ 2883135955142130412753230791844249602*t+1) Then for all i>=0 we have 3 3 3 7 a(i) + 32 b(i) + 32 c(i) = -28672 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 196, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 8803434666221251031 t + 49158876593055477506 t - 25 ) a(i) t = ---------------------------------------------------- / 2 ----- (t - 1) (t - 12479531931441057602 t + 1) i = 0 infinity ----- 2 \ i 9 (662433262103183689 t + 1285192049164338742 t + 1) ) b(i) t = - ----------------------------------------------------- / 2 ----- (t - 1) (t - 12479531931441057602 t + 1) i = 0 infinity ----- 2 \ i 16 (259339219742693845 t - 1354878457330675214 t + 1) ) c(i) t = ------------------------------------------------------ / 2 ----- (t - 1) (t - 12479531931441057602 t + 1) i = 0 In Maple notation, these generating functions are (8803434666221251031*t^2+49158876593055477506*t-25)/(t-1)/(t^2-\ 12479531931441057602*t+1) -9*(662433262103183689*t^2+1285192049164338742*t+1)/(t-1)/(t^2-\ 12479531931441057602*t+1) 16*(259339219742693845*t^2-1354878457330675214*t+1)/(t-1)/(t^2-\ 12479531931441057602*t+1) Then for all i>=0 we have 3 3 3 7 a(i) + 34 b(i) + 34 c(i) = -5103 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 197, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 22 (18957645062588966857046419596543359 t / ----- i = 0 / + 127566252310626797715010270852851842 t - 1) / ((t - 1) / 2 (t - 700766465697988439257662432584064002 t + 1)) infinity ----- \ i 2 ) b(i) t = - (248988938500137689957822054363109283 t / ----- i = 0 / + 1222620639465638032483269054063425114 t + 3) / ((t - 1) / 2 (t - 700766465697988439257662432584064002 t + 1)) infinity ----- \ i 2 ) c(i) t = (109966208041151933006148310655124653 t / ----- i = 0 / - 1581575786006927655447239419081659066 t + 13) / ((t - 1) / 2 (t - 700766465697988439257662432584064002 t + 1)) In Maple notation, these generating functions are 22*(18957645062588966857046419596543359*t^2+ 127566252310626797715010270852851842*t-1)/(t-1)/(t^2-\ 700766465697988439257662432584064002*t+1) -(248988938500137689957822054363109283*t^2+ 1222620639465638032483269054063425114*t+3)/(t-1)/(t^2-\ 700766465697988439257662432584064002*t+1) (109966208041151933006148310655124653*t^2-1581575786006927655447239419081659066 *t+13)/(t-1)/(t^2-700766465697988439257662432584064002*t+1) Then for all i>=0 we have 3 3 3 7 a(i) + 36 b(i) + 36 c(i) = -3584 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 198, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (970311134628635445375285564216875677 t / ----- i = 0 / + 5168455535358726244974277737182426110 t - 27) / ((t - 1) / 2 (t - 1195374478579885607948585577204664898 t + 1)) infinity ----- \ i 2 ) b(i) t = - 10 (64948353572425111714223068950383777 t / ----- i = 0 / + 106197025063390461784220084447077918 t + 1) / ((t - 1) / 2 (t - 1195374478579885607948585577204664898 t + 1)) infinity ----- \ i 2 ) c(i) t = (465911158902617384233392880057401833 t / ----- i = 0 / - 2177364945260773119217824414032018810 t + 17) / ((t - 1) / 2 (t - 1195374478579885607948585577204664898 t + 1)) In Maple notation, these generating functions are (970311134628635445375285564216875677*t^2+5168455535358726244974277737182426110 *t-27)/(t-1)/(t^2-1195374478579885607948585577204664898*t+1) -10*(64948353572425111714223068950383777*t^2+ 106197025063390461784220084447077918*t+1)/(t-1)/(t^2-\ 1195374478579885607948585577204664898*t+1) (465911158902617384233392880057401833*t^2-2177364945260773119217824414032018810 *t+17)/(t-1)/(t^2-1195374478579885607948585577204664898*t+1) Then for all i>=0 we have 3 3 3 7 a(i) + 37 b(i) + 37 c(i) = -7000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 199, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 65894051 t + 337432506 t - 29 ) a(i) t = ------------------------------ / 2 ----- (t - 1) (t - 71673154 t + 1) i = 0 infinity ----- 2 \ i 11 (3969433 t + 5510246 t + 1) ) b(i) t = - ------------------------------- / 2 ----- (t - 1) (t - 71673154 t + 1) i = 0 infinity ----- 2 \ i 2 (16066153 t - 68204402 t + 9) ) c(i) t = -------------------------------- / 2 ----- (t - 1) (t - 71673154 t + 1) i = 0 In Maple notation, these generating functions are (65894051*t^2+337432506*t-29)/(t-1)/(t^2-71673154*t+1) -11*(3969433*t^2+5510246*t+1)/(t-1)/(t^2-71673154*t+1) 2*(16066153*t^2-68204402*t+9)/(t-1)/(t^2-71673154*t+1) Then for all i>=0 we have 3 3 3 7 a(i) + 40 b(i) + 40 c(i) = -9317 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 200, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 25 (98123118799 t + 228925380402 t - 1) ) a(i) t = ---------------------------------------- / 2 ----- (t - 1) (t - 1000004000002 t + 1) i = 0 infinity ----- 2 \ i 1620524417209 t + 443304062782 t + 9 ) b(i) t = - ------------------------------------- / 2 ----- (t - 1) (t - 1000004000002 t + 1) i = 0 infinity ----- 2 \ i 16 (75106639201 t - 204095919202 t + 1) ) c(i) t = ---------------------------------------- / 2 ----- (t - 1) (t - 1000004000002 t + 1) i = 0 In Maple notation, these generating functions are 25*(98123118799*t^2+228925380402*t-1)/(t-1)/(t^2-1000004000002*t+1) -(1620524417209*t^2+443304062782*t+9)/(t-1)/(t^2-1000004000002*t+1) 16*(75106639201*t^2-204095919202*t+1)/(t-1)/(t^2-1000004000002*t+1) Then for all i>=0 we have 3 3 3 7 a(i) + 41 b(i) + 41 c(i) = -28672 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 201, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 27 (1032358562104520935800058189045511979535933319 t / ----- i = 0 / + 5540674178439037458750439906700367939825525242 t - 1) / ((t - 1) / 2 (t - 34409600437423270526222414743371961588245549122 t + 1)) infinity ----- \ i 2 ) b(i) t = - 9 (1942981448453385993015657241258531481471494201 t / ----- i = 0 / + 3538963324192802405491269443624364338252986438 t + 1) / ((t - 1) / 2 (t - 34409600437423270526222414743371961588245549122 t + 1)) infinity ----- \ i 2 ) c(i) t = 16 (763339618407471416905410242583596654050196236 t / ----- i = 0 / - 3846933553020952391065556502830225552645216597 t + 1) / ((t - 1) / 2 (t - 34409600437423270526222414743371961588245549122 t + 1)) In Maple notation, these generating functions are 27*(1032358562104520935800058189045511979535933319*t^2+ 5540674178439037458750439906700367939825525242*t-1)/(t-1)/(t^2-\ 34409600437423270526222414743371961588245549122*t+1) -9*(1942981448453385993015657241258531481471494201*t^2+ 3538963324192802405491269443624364338252986438*t+1)/(t-1)/(t^2-\ 34409600437423270526222414743371961588245549122*t+1) 16*(763339618407471416905410242583596654050196236*t^2-\ 3846933553020952391065556502830225552645216597*t+1)/(t-1)/(t^2-\ 34409600437423270526222414743371961588245549122*t+1) Then for all i>=0 we have 3 3 3 7 a(i) + 43 b(i) + 43 c(i) = -7000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 202, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 9 (6723197 t + 16029062 t - 3) ) a(i) t = ------------------------------- / 2 ----- (t - 1) (t - 23639042 t + 1) i = 0 infinity ----- 2 \ i 2 (19818629 t + 4308854 t + 5) ) b(i) t = - ------------------------------- / 2 ----- (t - 1) (t - 23639042 t + 1) i = 0 infinity ----- 2 \ i 17 (1765345 t - 4603874 t + 1) ) c(i) t = ------------------------------- / 2 ----- (t - 1) (t - 23639042 t + 1) i = 0 In Maple notation, these generating functions are 9*(6723197*t^2+16029062*t-3)/(t-1)/(t^2-23639042*t+1) -2*(19818629*t^2+4308854*t+5)/(t-1)/(t^2-23639042*t+1) 17*(1765345*t^2-4603874*t+1)/(t-1)/(t^2-23639042*t+1) Then for all i>=0 we have 3 3 3 7 a(i) + 44 b(i) + 44 c(i) = -34391 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 203, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = ( / ----- i = 0 2 52799407483181700357140309238736469230740007092983105589311617649737 t + 349533357961301095820378738611878832059409710678884540032263632897422 t / 2 - 23) / ((t - 1) (t / - 114788157491908303544462754035400505288572007286006549974131636658754 t + 1)) infinity ----- \ i ) b(i) t = - ( / ----- i = 0 2 48313592619826330743850851585322161690402505043384334395386735560129 t - 8118597023564966710892240715374867080064046084253884547370178654866 t / 2 + 17) / ((t - 1) (t / - 114788157491908303544462754035400505288572007286006549974131636658754 t + 1)) infinity ----- \ i ) c(i) t = ( / ----- i = 0 2 44793632120947550720041497636073063741686504570518794022765961050147 t - 84988627717208914753000108506020358352024963529649243870782517955446 t / 2 + 19) / ((t - 1) (t / - 114788157491908303544462754035400505288572007286006549974131636658754 t + 1)) In Maple notation, these generating functions are (52799407483181700357140309238736469230740007092983105589311617649737*t^2+ 349533357961301095820378738611878832059409710678884540032263632897422*t-23)/(t-\ 1)/(t^2-114788157491908303544462754035400505288572007286006549974131636658754*t +1) -(48313592619826330743850851585322161690402505043384334395386735560129*t^2-\ 8118597023564966710892240715374867080064046084253884547370178654866*t+17)/(t-1) /(t^2-114788157491908303544462754035400505288572007286006549974131636658754*t+1 ) (44793632120947550720041497636073063741686504570518794022765961050147*t^2-\ 84988627717208914753000108506020358352024963529649243870782517955446*t+19)/(t-1 )/(t^2-114788157491908303544462754035400505288572007286006549974131636658754*t+ 1) Then for all i>=0 we have 3 3 3 7 a(i) + 45 b(i) + 45 c(i) = -2401 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 204, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = (72201309111754699635220014433764115891559792497651669740\ / ----- i = 0 2 44754365474363126851 t + 1754667083068034917887296903692669942362198370\ / 2 9872707573857309888338782524378 t - 29) / ((t - 1) (t - 2706587653977\ / 154476086667731393471090083824099275402378583879792531106022402 t + 1)) infinity ----- \ i ) b(i) t = - (469463945671263735330149732020254448268489881718818888\ / ----- i = 0 2 5688884485706995530091 t + 777676038969407306099406164028297373059862642664639003001363425310146793098 / 2 t + 11) / ((t - 1) (t - 270658765397715447608666773139347109008382409\ / 9275402378583879792531106022402 t + 1)) infinity ----- \ i ) c(i) t = 18 ( / ----- i = 0 201072267242630810709830217430123770167964999597504383935064172895872633601 2 t - 505089794780522180676547077665170539931562858478217044417855723507936096002 / 2 t + 1) / ((t - 1) (t - 2706587653977154476086667731393471090083824099\ / 275402378583879792531106022402 t + 1)) In Maple notation, these generating functions are (7220130911175469963522001443376411589155979249765166974044754365474363126851*t ^2+ 17546670830680349178872969036926699423621983709872707573857309888338782524378*t -29)/(t-1)/(t^2-\ 2706587653977154476086667731393471090083824099275402378583879792531106022402*t+ 1) -(4694639456712637353301497320202544482684898817188188885688884485706995530091* t^2+777676038969407306099406164028297373059862642664639003001363425310146793098 *t+11)/(t-1)/(t^2-\ 2706587653977154476086667731393471090083824099275402378583879792531106022402*t+ 1) 18*(201072267242630810709830217430123770167964999597504383935064172895872633601 *t^2-\ 505089794780522180676547077665170539931562858478217044417855723507936096002*t+1 )/(t-1)/(t^2-\ 2706587653977154476086667731393471090083824099275402378583879792531106022402*t+ 1) Then for all i>=0 we have 3 3 3 7 a(i) + 47 b(i) + 47 c(i) = -40824 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 205, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 3 ( / ----- i = 0 2 1262068102468076768951332394711 t + 3396580416236494669396786480498 t - 9) / 2 / ((t - 1) (t - 1508944233534243168787365384002 t + 1)) / infinity ----- \ i ) b(i) t = - 4 / ----- i = 0 2 (513472893132197938556688265261 t + 724902029561422317206735739538 t + 1) / 2 / ((t - 1) (t - 1508944233534243168787365384002 t + 1)) / infinity ----- \ i ) c(i) t = 15 / ----- i = 0 2 (73822699711848945167550251001 t - 404056012430147680037796652282 t + 1) / 2 / ((t - 1) (t - 1508944233534243168787365384002 t + 1)) / In Maple notation, these generating functions are 3*(1262068102468076768951332394711*t^2+3396580416236494669396786480498*t-9)/(t-\ 1)/(t^2-1508944233534243168787365384002*t+1) -4*(513472893132197938556688265261*t^2+724902029561422317206735739538*t+1)/(t-1 )/(t^2-1508944233534243168787365384002*t+1) 15*(73822699711848945167550251001*t^2-404056012430147680037796652282*t+1)/(t-1) /(t^2-1508944233534243168787365384002*t+1) Then for all i>=0 we have 3 3 3 7 a(i) + 52 b(i) + 52 c(i) = -34391 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 206, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 4 / ----- i = 0 2 (66401924560158657219152641049 t + 92229039756044835266933611502 t - 7) / 2 / ((t - 1) (t - 52002250624926938286289585154 t + 1)) / infinity ----- \ i ) b(i) t = - 2 / ----- i = 0 2 (77859085107944961344988702149 t - 14503099022168887202166272458 t + 5) / 2 / ((t - 1) (t - 52002250624926938286289585154 t + 1)) / infinity ----- \ i ) c(i) t = / ----- i = 0 2 119963287760419876495049059121 t - 246675259931972024780693918530 t + 17 ------------------------------------------------------------------------- 2 (t - 1) (t - 52002250624926938286289585154 t + 1) In Maple notation, these generating functions are 4*(66401924560158657219152641049*t^2+92229039756044835266933611502*t-7)/(t-1)/( t^2-52002250624926938286289585154*t+1) -2*(77859085107944961344988702149*t^2-14503099022168887202166272458*t+5)/(t-1)/ (t^2-52002250624926938286289585154*t+1) (119963287760419876495049059121*t^2-246675259931972024780693918530*t+17)/(t-1)/ (t^2-52002250624926938286289585154*t+1) Then for all i>=0 we have 3 3 3 7 a(i) + 64 b(i) + 64 c(i) = -96768 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 207, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 247876177 t + 271756102 t - 23 ) a(i) t = ------------------------------- / 2 ----- (t - 1) (t - 47141954 t + 1) i = 0 infinity ----- 2 \ i 3 (63363789 t - 46066514 t + 5) ) b(i) t = - -------------------------------- / 2 ----- (t - 1) (t - 47141954 t + 1) i = 0 infinity ----- 2 \ i 6 (28927715 t - 37576358 t + 3) ) c(i) t = -------------------------------- / 2 ----- (t - 1) (t - 47141954 t + 1) i = 0 In Maple notation, these generating functions are (247876177*t^2+271756102*t-23)/(t-1)/(t^2-47141954*t+1) -3*(63363789*t^2-46066514*t+5)/(t-1)/(t^2-47141954*t+1) 6*(28927715*t^2-37576358*t+3)/(t-1)/(t^2-47141954*t+1) Then for all i>=0 we have 3 3 3 7 a(i) + 65 b(i) + 65 c(i) = -74536 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 208, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (15657436859 t + 37474657106 t - 13) ) a(i) t = --------------------------------------- / 2 ----- (t - 1) (t - 13281640514 t + 1) i = 0 infinity ----- 2 \ i 2 (18453090725 t - 16555647666 t + 13) ) b(i) t = - --------------------------------------- / 2 ----- (t - 1) (t - 13281640514 t + 1) i = 0 infinity ----- 2 \ i 36160589219 t - 39955475390 t + 27 ) c(i) t = ----------------------------------- / 2 ----- (t - 1) (t - 13281640514 t + 1) i = 0 In Maple notation, these generating functions are 2*(15657436859*t^2+37474657106*t-13)/(t-1)/(t^2-13281640514*t+1) -2*(18453090725*t^2-16555647666*t+13)/(t-1)/(t^2-13281640514*t+1) (36160589219*t^2-39955475390*t+27)/(t-1)/(t^2-13281640514*t+1) Then for all i>=0 we have 3 3 3 7 a(i) + 72 b(i) + 72 c(i) = -28672 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 209, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 4 (648028818578856341501152834818060065446010712103241146\ / ----- i = 0 2 2480686962192545618172793 t + 30300076679361367447113020119904933506519\ / 2 207990132211958459126942334604294505614 t - 7) / ((t - 1) (t - 229123\ / 584405852028321431613407745950511018684299058309835362775142956015849472\ 02 t + 1)) infinity ----- \ i ) b(i) t = - 5 (2475427170684873463766680334012879822575779810764901\ / ----- i = 0 2 895715119361784734245405633 t + 596596804426756968491764226521986572256\ / 2 7013821305667414008772354008382127995966 t + 1) / ((t - 1) (t - 22912\ / 358440585202832143161340774595051101868429905830983536277514295601584947\ 202 t + 1)) infinity ----- \ i ) c(i) t = (71929053047935165868241789915199185893108133569985803085\ / ----- i = 0 2 91047239169634732489933 t - 4939988137955573233024579198768364631502478\ / 2 1517351426857210505818135216599497946 t + 13) / ((t - 1) (t - 2291235\ / 844058520283214316134077459505110186842990583098353627751429560158494720\ 2 t + 1)) In Maple notation, these generating functions are 4*(6480288185788563415011528348180600654460107121032411462480686962192545618172\ 793*t^2+30300076679361367447113020119904933506519207990132211958459126942334604\ 294505614*t-7)/(t-1)/(t^2-22912358440585202832143161340774595051101868429905830\ 983536277514295601584947202*t+1) -5*(247542717068487346376668033401287982257577981076490189571511936178473424540\ 5633*t^2+5965968044267569684917642265219865722567013821305667414008772354008382\ 127995966*t+1)/(t-1)/(t^2-22912358440585202832143161340774595051101868429905830\ 983536277514295601584947202*t+1) (719290530479351658682417899151991858931081335699858030859104723916963473248993\ 3*t^2-4939988137955573233024579198768364631502478151735142685721050581813521659\ 9497946*t+13)/(t-1)/(t^2-229123584405852028321431613407745950511018684299058309\ 83536277514295601584947202*t+1) Then for all i>=0 we have 3 3 3 7 a(i) + 80 b(i) + 80 c(i) = -12096 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 210, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (72914781205733513417949114902069476755983977 t / ----- i = 0 / + 598130807818527000493540477698233580808176046 t - 23) / ((t - 1) / 2 (t - 170013971597385835683936720467301082821120002 t + 1)) infinity ----- \ i 2 ) b(i) t = - 3 (10770084723765886237685679489418964288366401 t / ----- i = 0 / + 61607713784243722350610578572247004940433598 t + 1) / ((t - 1) / 2 (t - 170013971597385835683936720467301082821120002 t + 1)) infinity ----- \ i 2 ) c(i) t = 10 (1529680522329317224886891165777401495536961 t / ----- i = 0 / - 23243020074732199801375768584277192264176962 t + 1) / ((t - 1) / 2 (t - 170013971597385835683936720467301082821120002 t + 1)) In Maple notation, these generating functions are (72914781205733513417949114902069476755983977*t^2+ 598130807818527000493540477698233580808176046*t-23)/(t-1)/(t^2-\ 170013971597385835683936720467301082821120002*t+1) -3*(10770084723765886237685679489418964288366401*t^2+ 61607713784243722350610578572247004940433598*t+1)/(t-1)/(t^2-\ 170013971597385835683936720467301082821120002*t+1) 10*(1529680522329317224886891165777401495536961*t^2-\ 23243020074732199801375768584277192264176962*t+1)/(t-1)/(t^2-\ 170013971597385835683936720467301082821120002*t+1) Then for all i>=0 we have 3 3 3 7 a(i) + 90 b(i) + 90 c(i) = -2401 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 211, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 26 / ----- i = 0 2 (200419162362376712894637441791 t + 328902315016410737283709156610 t - 1) / 2 / ((t - 1) (t - 1375121480179839396884378320898 t + 1)) / infinity ----- \ i ) b(i) t = - ( / ----- i = 0 2 4092632229075288556534725396113 t - 3195571620043869825179843266210 t + 17 / 2 ) / ((t - 1) (t - 1375121480179839396884378320898 t + 1)) / infinity ----- \ i ) c(i) t = 19 / ----- i = 0 2 (203477444044187282071025424769 t - 250691160308998794247598168450 t + 1) / 2 / ((t - 1) (t - 1375121480179839396884378320898 t + 1)) / In Maple notation, these generating functions are 26*(200419162362376712894637441791*t^2+328902315016410737283709156610*t-1)/(t-1 )/(t^2-1375121480179839396884378320898*t+1) -(4092632229075288556534725396113*t^2-3195571620043869825179843266210*t+17)/(t-\ 1)/(t^2-1375121480179839396884378320898*t+1) 19*(203477444044187282071025424769*t^2-250691160308998794247598168450*t+1)/(t-1 )/(t^2-1375121480179839396884378320898*t+1) Then for all i>=0 we have 3 3 3 7 a(i) + 92 b(i) + 92 c(i) = -56000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 212, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 2 / ----- i = 0 2 (5008581648509606171814356987 t + 721801260735713288881547643026 t - 13) / 2 / ((t - 1) (t - 2046178027603990570787172000002 t + 1)) / infinity ----- \ i ) b(i) t = - 2 / ----- i = 0 2 (2121584698262252295983943001 t + 289528224666107444445174056998 t + 1) / 2 / ((t - 1) (t - 2046178027603990570787172000002 t + 1)) / infinity ----- \ i ) c(i) t = / ----- i = 0 2 904114964184767144091648011 t - 584203733692924160626407648022 t + 11 ---------------------------------------------------------------------- 2 (t - 1) (t - 2046178027603990570787172000002 t + 1) In Maple notation, these generating functions are 2*(5008581648509606171814356987*t^2+721801260735713288881547643026*t-13)/(t-1)/ (t^2-2046178027603990570787172000002*t+1) -2*(2121584698262252295983943001*t^2+289528224666107444445174056998*t+1)/(t-1)/ (t^2-2046178027603990570787172000002*t+1) (904114964184767144091648011*t^2-584203733692924160626407648022*t+11)/(t-1)/(t^ 2-2046178027603990570787172000002*t+1) Then for all i>=0 we have 3 3 3 7 a(i) + 93 b(i) + 93 c(i) = -7 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 213, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 8 (469753295342737943419778617749965770062300654944 t / ----- i = 0 / + 707988314446616574816221915573895644655494607449 t - 1) / ((t - 1) / 2 (t - 2484063604387302909543062681203405724886778393154 t + 1)) infinity ----- \ i 2 ) b(i) t = - (1674763153172491466923580499491682877816946659969 t / ----- i = 0 / + 1006274657730104184345363804009790261378034425150 t + 1) / ((t - 1) / 2 (t - 2484063604387302909543062681203405724886778393154 t + 1)) infinity ----- \ i 2 ) c(i) t = 4 (230789470156027689362983677772934411429316403015 t / ----- i = 0 / - 901048922881676602180219753648302696228061674296 t + 1) / ((t - 1) / 2 (t - 2484063604387302909543062681203405724886778393154 t + 1)) In Maple notation, these generating functions are 8*(469753295342737943419778617749965770062300654944*t^2+ 707988314446616574816221915573895644655494607449*t-1)/(t-1)/(t^2-\ 2484063604387302909543062681203405724886778393154*t+1) -(1674763153172491466923580499491682877816946659969*t^2+ 1006274657730104184345363804009790261378034425150*t+1)/(t-1)/(t^2-\ 2484063604387302909543062681203405724886778393154*t+1) 4*(230789470156027689362983677772934411429316403015*t^2-\ 901048922881676602180219753648302696228061674296*t+1)/(t-1)/(t^2-\ 2484063604387302909543062681203405724886778393154*t+1) Then for all i>=0 we have 3 3 3 7 a(i) + 95 b(i) + 95 c(i) = -2401 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 214, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 2 (1130538827388154724978967479234683463 t / ----- i = 0 / + 10430370748222636422890852322940653350 t - 13) / ((t - 1) / 2 (t - 5979707330721452527359025689383224898 t + 1)) infinity ----- \ i 2 ) b(i) t = - 4 (245169353363167803935186911374229407 t / ----- i = 0 / + 1477779105969795263908637846240288528 t + 1) / ((t - 1) / 2 (t - 5979707330721452527359025689383224898 t + 1)) infinity ----- \ i 2 ) c(i) t = 11 (45550443692848440687986577388740257 t / ----- i = 0 / - 672077156177562283540286489248564962 t + 1) / ((t - 1) / 2 (t - 5979707330721452527359025689383224898 t + 1)) In Maple notation, these generating functions are 2*(1130538827388154724978967479234683463*t^2+ 10430370748222636422890852322940653350*t-13)/(t-1)/(t^2-\ 5979707330721452527359025689383224898*t+1) -4*(245169353363167803935186911374229407*t^2+ 1477779105969795263908637846240288528*t+1)/(t-1)/(t^2-\ 5979707330721452527359025689383224898*t+1) 11*(45550443692848440687986577388740257*t^2-\ 672077156177562283540286489248564962*t+1)/(t-1)/(t^2-\ 5979707330721452527359025689383224898*t+1) Then for all i>=0 we have 3 3 3 7 a(i) + 99 b(i) + 99 c(i) = -2401 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 215, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 25 (303666454066121502179284335192409532755438079 t / ----- i = 0 / + 1023244052273943979737609638173787073028753922 t - 1) / ((t - 1) / 2 (t - 3756915289035125159644217876398267498304640002 t + 1)) infinity ----- \ i 2 ) b(i) t = - (3202607266418450335800423599339690221869170401 t / ----- i = 0 / + 7988204232835113969522778585676425730527629598 t + 1) / ((t - 1) / 2 (t - 3756915289035125159644217876398267498304640002 t + 1)) infinity ----- \ i 2 ) c(i) t = 11 (118608357136835540652717864035193694740698401 t / ----- i = 0 / - 1135954857068977750227554426309386054049498402 t + 1) / ((t - 1) / 2 (t - 3756915289035125159644217876398267498304640002 t + 1)) In Maple notation, these generating functions are 25*(303666454066121502179284335192409532755438079*t^2+ 1023244052273943979737609638173787073028753922*t-1)/(t-1)/(t^2-\ 3756915289035125159644217876398267498304640002*t+1) -(3202607266418450335800423599339690221869170401*t^2+ 7988204232835113969522778585676425730527629598*t+1)/(t-1)/(t^2-\ 3756915289035125159644217876398267498304640002*t+1) 11*(118608357136835540652717864035193694740698401*t^2-\ 1135954857068977750227554426309386054049498402*t+1)/(t-1)/(t^2-\ 3756915289035125159644217876398267498304640002*t+1) Then for all i>=0 we have 3 3 3 7 a(i) + 100 b(i) + 100 c(i) = -23625 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 216, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (337902185594712926641271226827054443 t / ----- i = 0 / + 9254316909642222843821611531511910322 t - 29) / ((t - 1) / 2 (t - 3768371787414510481253275369347450434 t + 1)) infinity ----- \ i 2 ) b(i) t = - 2 (164155935018615945193150811093351435 t / ----- i = 0 / + 3946795105797213670719513228194776306 t + 3) / ((t - 1) / 2 (t - 3768371787414510481253275369347450434 t + 1)) infinity ----- \ i 2 ) c(i) t = 4 (25760936576855818156363534408833311 t / ----- i = 0 / - 2081236456984770626112695554052897190 t + 7) / ((t - 1) / 2 (t - 3768371787414510481253275369347450434 t + 1)) In Maple notation, these generating functions are (337902185594712926641271226827054443*t^2+9254316909642222843821611531511910322 *t-29)/(t-1)/(t^2-3768371787414510481253275369347450434*t+1) -2*(164155935018615945193150811093351435*t^2+ 3946795105797213670719513228194776306*t+3)/(t-1)/(t^2-\ 3768371787414510481253275369347450434*t+1) 4*(25760936576855818156363534408833311*t^2-\ 2081236456984770626112695554052897190*t+7)/(t-1)/(t^2-\ 3768371787414510481253275369347450434*t+1) Then for all i>=0 we have 3 3 3 8 a(i) + 9 b(i) + 9 c(i) = -512 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 217, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 1968551527 t + 3332897202 t - 25 ) a(i) t = --------------------------------- / 2 ----- (t - 1) (t - 554602498 t + 1) i = 0 infinity ----- 2 \ i 2 (1224848651 t - 504898838 t + 11) ) b(i) t = - ------------------------------------ / 2 ----- (t - 1) (t - 554602498 t + 1) i = 0 infinity ----- 2 \ i 2 (1045889423 t - 1765839262 t + 15) ) c(i) t = ------------------------------------- / 2 ----- (t - 1) (t - 554602498 t + 1) i = 0 In Maple notation, these generating functions are (1968551527*t^2+3332897202*t-25)/(t-1)/(t^2-554602498*t+1) -2*(1224848651*t^2-504898838*t+11)/(t-1)/(t^2-554602498*t+1) 2*(1045889423*t^2-1765839262*t+15)/(t-1)/(t^2-554602498*t+1) Then for all i>=0 we have 3 3 3 8 a(i) + 11 b(i) + 11 c(i) = -54872 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 218, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 30 / ----- i = 0 2 (91457757777101650995832887803 t + 760558022177257933677763959398 t - 1) / 2 / ((t - 1) (t - 5049846951510313885417026062402 t + 1)) / infinity ----- \ i ) b(i) t = - 8 / ----- i = 0 2 (303177880123027790782910447191 t + 1745161426479576416206353206008 t + 1) / 2 / ((t - 1) (t - 5049846951510313885417026062402 t + 1)) / infinity ----- \ i ) c(i) t = 26 / ----- i = 0 2 (44580186783776902550807002081 t - 674838434969193581624426587682 t + 1) / 2 / ((t - 1) (t - 5049846951510313885417026062402 t + 1)) / In Maple notation, these generating functions are 30*(91457757777101650995832887803*t^2+760558022177257933677763959398*t-1)/(t-1) /(t^2-5049846951510313885417026062402*t+1) -8*(303177880123027790782910447191*t^2+1745161426479576416206353206008*t+1)/(t-\ 1)/(t^2-5049846951510313885417026062402*t+1) 26*(44580186783776902550807002081*t^2-674838434969193581624426587682*t+1)/(t-1) /(t^2-5049846951510313885417026062402*t+1) Then for all i>=0 we have 3 3 3 8 a(i) + 13 b(i) + 13 c(i) = -5832 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 219, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 88364999949336921211 t + 253012234560012001186 t - 29 ) a(i) t = ------------------------------------------------------ / 2 ----- (t - 1) (t - 42530229188456857154 t + 1) i = 0 infinity ----- 2 \ i 2 (53934705541596771061 t - 19872675490774816514 t + 13) ) b(i) t = - --------------------------------------------------------- / 2 ----- (t - 1) (t - 42530229188456857154 t + 1) i = 0 infinity ----- 2 \ i 32 (3002731596560894353 t - 5131608474737266514 t + 1) ) c(i) t = ------------------------------------------------------- / 2 ----- (t - 1) (t - 42530229188456857154 t + 1) i = 0 In Maple notation, these generating functions are (88364999949336921211*t^2+253012234560012001186*t-29)/(t-1)/(t^2-\ 42530229188456857154*t+1) -2*(53934705541596771061*t^2-19872675490774816514*t+13)/(t-1)/(t^2-\ 42530229188456857154*t+1) 32*(3002731596560894353*t^2-5131608474737266514*t+1)/(t-1)/(t^2-\ 42530229188456857154*t+1) Then for all i>=0 we have 3 3 3 8 a(i) + 15 b(i) + 15 c(i) = -32768 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 220, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 30 (1499017295 t + 3282128306 t - 1) ) a(i) t = ------------------------------------- / 2 ----- (t - 1) (t - 12745958402 t + 1) i = 0 infinity ----- 2 \ i 8 (4695516841 t + 4372854358 t + 1) ) b(i) t = - ------------------------------------ / 2 ----- (t - 1) (t - 12745958402 t + 1) i = 0 infinity ----- 2 \ i 2 (10846093453 t - 47119578266 t + 13) ) c(i) t = --------------------------------------- / 2 ----- (t - 1) (t - 12745958402 t + 1) i = 0 In Maple notation, these generating functions are 30*(1499017295*t^2+3282128306*t-1)/(t-1)/(t^2-12745958402*t+1) -8*(4695516841*t^2+4372854358*t+1)/(t-1)/(t^2-12745958402*t+1) 2*(10846093453*t^2-47119578266*t+13)/(t-1)/(t^2-12745958402*t+1) Then for all i>=0 we have 3 3 3 8 a(i) + 17 b(i) + 17 c(i) = -74088 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 221, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (1882844851 t + 16383689158 t - 9) ) a(i) t = ------------------------------------- / 2 ----- (t - 1) (t - 13362897602 t + 1) i = 0 infinity ----- 2 \ i 5 (559178621 t + 3035518978 t + 1) ) b(i) t = - ----------------------------------- / 2 ----- (t - 1) (t - 13362897602 t + 1) i = 0 infinity ----- 2 \ i 13 (114314461 t - 1496890462 t + 1) ) c(i) t = ------------------------------------ / 2 ----- (t - 1) (t - 13362897602 t + 1) i = 0 In Maple notation, these generating functions are 2*(1882844851*t^2+16383689158*t-9)/(t-1)/(t^2-13362897602*t+1) -5*(559178621*t^2+3035518978*t+1)/(t-1)/(t^2-13362897602*t+1) 13*(114314461*t^2-1496890462*t+1)/(t-1)/(t^2-13362897602*t+1) Then for all i>=0 we have 3 3 3 8 a(i) + 23 b(i) + 23 c(i) = -1000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 222, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 27 / ----- i = 0 2 (6897533244817111178672699399 t + 24940307405264851587439800602 t - 1) / 2 / ((t - 1) (t - 99945349368737297515380360002 t + 1)) / infinity ----- \ i ) b(i) t = - 3 / ----- i = 0 2 (42686783233096901982471530101 t + 107078419184888650869321669898 t + 1) / 2 / ((t - 1) (t - 99945349368737297515380360002 t + 1)) / infinity ----- \ i ) c(i) t = / ----- i = 0 2 57114293466886133823923967919 t - 506409900720842792379303567938 t + 19 ------------------------------------------------------------------------ 2 (t - 1) (t - 99945349368737297515380360002 t + 1) In Maple notation, these generating functions are 27*(6897533244817111178672699399*t^2+24940307405264851587439800602*t-1)/(t-1)/( t^2-99945349368737297515380360002*t+1) -3*(42686783233096901982471530101*t^2+107078419184888650869321669898*t+1)/(t-1) /(t^2-99945349368737297515380360002*t+1) (57114293466886133823923967919*t^2-506409900720842792379303567938*t+19)/(t-1)/( t^2-99945349368737297515380360002*t+1) Then for all i>=0 we have 3 3 3 8 a(i) + 27 b(i) + 27 c(i) = -27000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 223, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (37225 t + 256114 t - 11) ) a(i) t = ---------------------------- / 2 ----- (t - 1) (t - 158402 t + 1) i = 0 infinity ----- 2 \ i 7 (7549 t + 25858 t + 1) ) b(i) t = - --------------------------- / 2 ----- (t - 1) (t - 158402 t + 1) i = 0 infinity ----- 2 \ i 3 (10769 t - 88726 t + 5) ) c(i) t = --------------------------- / 2 ----- (t - 1) (t - 158402 t + 1) i = 0 In Maple notation, these generating functions are 2*(37225*t^2+256114*t-11)/(t-1)/(t^2-158402*t+1) -7*(7549*t^2+25858*t+1)/(t-1)/(t^2-158402*t+1) 3*(10769*t^2-88726*t+5)/(t-1)/(t^2-158402*t+1) Then for all i>=0 we have 3 3 3 8 a(i) + 29 b(i) + 29 c(i) = -2744 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 224, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (562462931879306805070821340181944871750123765368099 t / ----- i = 0 / + 3208567677719283234139156254959297475996735305095930 t - 29) / ( / 2 (t - 1) (t - 746280566062256564369757600014731282242242822148098 t + 1)) infinity ----- \ i 2 ) b(i) t = - 16 (28944326420206982082611897019631603894003193782129 t / ----- i = 0 / + 25064501802010112546751341419255680577964533582990 t + 1) / ((t - 1) / 2 (t - 746280566062256564369757600014731282242242822148098 t + 1)) infinity ----- \ i 2 ) c(i) t = 22 (17117111998756778542103608040977216316267191524289 t / ----- i = 0 / - 56396259796732847363458690541986150477698265971650 t + 1) / ((t - 1) / 2 (t - 746280566062256564369757600014731282242242822148098 t + 1)) In Maple notation, these generating functions are (562462931879306805070821340181944871750123765368099*t^2+ 3208567677719283234139156254959297475996735305095930*t-29)/(t-1)/(t^2-\ 746280566062256564369757600014731282242242822148098*t+1) -16*(28944326420206982082611897019631603894003193782129*t^2+ 25064501802010112546751341419255680577964533582990*t+1)/(t-1)/(t^2-\ 746280566062256564369757600014731282242242822148098*t+1) 22*(17117111998756778542103608040977216316267191524289*t^2-\ 56396259796732847363458690541986150477698265971650*t+1)/(t-1)/(t^2-\ 746280566062256564369757600014731282242242822148098*t+1) Then for all i>=0 we have 3 3 3 8 a(i) + 31 b(i) + 31 c(i) = -8000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 225, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 30 (26914928482000734455543 t + 677293786149228542731658 t - 1) ---------------------------------------------------------------- 2 (t - 1) (t - 13825485377045766625593602 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 16 (38127002885359452099871 t + 317570256035516560356928 t + 1) - ---------------------------------------------------------------- 2 (t - 1) (t - 13825485377045766625593602 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 2 (231611672677419068283851 t - 3077189744044427167938262 t + 11) ------------------------------------------------------------------ 2 (t - 1) (t - 13825485377045766625593602 t + 1) In Maple notation, these generating functions are 30*(26914928482000734455543*t^2+677293786149228542731658*t-1)/(t-1)/(t^2-\ 13825485377045766625593602*t+1) -16*(38127002885359452099871*t^2+317570256035516560356928*t+1)/(t-1)/(t^2-\ 13825485377045766625593602*t+1) 2*(231611672677419068283851*t^2-3077189744044427167938262*t+11)/(t-1)/(t^2-\ 13825485377045766625593602*t+1) Then for all i>=0 we have 3 3 3 8 a(i) + 33 b(i) + 33 c(i) = -216 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 226, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 2 (1082394036383571827190647 t + 6454533462918800968880582 t - 13) ------------------------------------------------------------------- 2 (t - 1) (t - 3221831643828009797737154 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 9 (165450697031144305651333 t + 394172665420371043831546 t + 1) - ---------------------------------------------------------------- 2 (t - 1) (t - 3221831643828009797737154 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 994247570933523058431989 t - 6030857832997161203777926 t + 17 -------------------------------------------------------------- 2 (t - 1) (t - 3221831643828009797737154 t + 1) In Maple notation, these generating functions are 2*(1082394036383571827190647*t^2+6454533462918800968880582*t-13)/(t-1)/(t^2-\ 3221831643828009797737154*t+1) -9*(165450697031144305651333*t^2+394172665420371043831546*t+1)/(t-1)/(t^2-\ 3221831643828009797737154*t+1) (994247570933523058431989*t^2-6030857832997161203777926*t+17)/(t-1)/(t^2-\ 3221831643828009797737154*t+1) Then for all i>=0 we have 3 3 3 8 a(i) + 35 b(i) + 35 c(i) = -5832 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 227, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (76396206896533 t + 413771618220298 t - 15) ) a(i) t = ---------------------------------------------- / 2 ----- (t - 1) (t - 173248299913922 t + 1) i = 0 infinity ----- 2 \ i 11 (9336408556861 t + 16260637556546 t + 1) ) b(i) t = - -------------------------------------------- / 2 ----- (t - 1) (t - 173248299913922 t + 1) i = 0 infinity ----- 2 \ i 72887340214631 t - 354454847462138 t + 19 ) c(i) t = ------------------------------------------ / 2 ----- (t - 1) (t - 173248299913922 t + 1) i = 0 In Maple notation, these generating functions are 2*(76396206896533*t^2+413771618220298*t-15)/(t-1)/(t^2-173248299913922*t+1) -11*(9336408556861*t^2+16260637556546*t+1)/(t-1)/(t^2-173248299913922*t+1) (72887340214631*t^2-354454847462138*t+19)/(t-1)/(t^2-173248299913922*t+1) Then for all i>=0 we have 3 3 3 8 a(i) + 41 b(i) + 41 c(i) = -10648 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 228, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 34170734659189817699 t + 119257364945018568378 t - 29 ) a(i) t = ------------------------------------------------------ / 2 ----- (t - 1) (t - 21909411743967887362 t + 1) i = 0 infinity ----- 2 \ i 28 (1437463086158381569 t - 1055270508068880898 t + 1) ) b(i) t = - ------------------------------------------------------- / 2 ----- (t - 1) (t - 21909411743967887362 t + 1) i = 0 infinity ----- 2 \ i 2 (19329814958329206671 t - 24680511051582216094 t + 15) ) c(i) t = --------------------------------------------------------- / 2 ----- (t - 1) (t - 21909411743967887362 t + 1) i = 0 In Maple notation, these generating functions are (34170734659189817699*t^2+119257364945018568378*t-29)/(t-1)/(t^2-\ 21909411743967887362*t+1) -28*(1437463086158381569*t^2-1055270508068880898*t+1)/(t-1)/(t^2-\ 21909411743967887362*t+1) 2*(19329814958329206671*t^2-24680511051582216094*t+15)/(t-1)/(t^2-\ 21909411743967887362*t+1) Then for all i>=0 we have 3 3 3 8 a(i) + 43 b(i) + 43 c(i) = -21952 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 229, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (9893 t + 352514 t - 7) ) a(i) t = ---------------------------- / 2 ----- (t - 1) (t - 1435202 t + 1) i = 0 infinity ----- 2 \ i 8 (1811 t + 16188 t + 1) ) b(i) t = - ---------------------------- / 2 ----- (t - 1) (t - 1435202 t + 1) i = 0 infinity ----- 2 \ i 10 (1185 t - 15586 t + 1) ) c(i) t = ---------------------------- / 2 ----- (t - 1) (t - 1435202 t + 1) i = 0 In Maple notation, these generating functions are 2*(9893*t^2+352514*t-7)/(t-1)/(t^2-1435202*t+1) -8*(1811*t^2+16188*t+1)/(t-1)/(t^2-1435202*t+1) 10*(1185*t^2-15586*t+1)/(t-1)/(t^2-1435202*t+1) Then for all i>=0 we have 3 3 3 8 a(i) + 45 b(i) + 45 c(i) = -8 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 230, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 10 (8880545861380897 t + 21007879119666226 t - 3) ) a(i) t = -------------------------------------------------- / 2 ----- (t - 1) (t - 30840804542712002 t + 1) i = 0 infinity ----- 2 \ i 58350160066938031 t + 13883271453225158 t + 11 ) b(i) t = - ----------------------------------------------- / 2 ----- (t - 1) (t - 30840804542712002 t + 1) i = 0 infinity ----- 2 \ i 19 (2307963667421581 t - 6109723221114382 t + 1) ) c(i) t = ------------------------------------------------- / 2 ----- (t - 1) (t - 30840804542712002 t + 1) i = 0 In Maple notation, these generating functions are 10*(8880545861380897*t^2+21007879119666226*t-3)/(t-1)/(t^2-30840804542712002*t+ 1) -(58350160066938031*t^2+13883271453225158*t+11)/(t-1)/(t^2-30840804542712002*t+ 1) 19*(2307963667421581*t^2-6109723221114382*t+1)/(t-1)/(t^2-30840804542712002*t+1 ) Then for all i>=0 we have 3 3 3 8 a(i) + 49 b(i) + 49 c(i) = -54872 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 231, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 27 ( / ----- i = 0 2 347217810101271112482506831836311056576438175616279026690108646026303 t + 443072526809066606279728119380604085872814070988082835216639137256386 t / 2 - 1) / ((t - 1) (t / - 1764380986686440298536082635279244499396706231285168468374854076403714 t + 1)) infinity ----- \ i ) b(i) t = - 2 ( / ----- i = 0 2 3396634567835829044285249819266915196071700735894932368777865381134919 t - 1523605662628367703948593144868133524552560729743114324293198087537230 t / 2 + 7) / ((t - 1) (t / - 1764380986686440298536082635279244499396706231285168468374854076403714 t + 1)) infinity ----- \ i ) c(i) t = 4 ( / ----- i = 0 2 1422585493543375697524163601998739994283972993193362251429140530487749 t - 2359099946147106367692491939198130830043542996269271273671474177286602 t / 2 + 5) / ((t - 1) (t / - 1764380986686440298536082635279244499396706231285168468374854076403714 t + 1)) In Maple notation, these generating functions are 27*(347217810101271112482506831836311056576438175616279026690108646026303*t^2+ 443072526809066606279728119380604085872814070988082835216639137256386*t-1)/(t-1 )/(t^2-1764380986686440298536082635279244499396706231285168468374854076403714*t +1) -2*(3396634567835829044285249819266915196071700735894932368777865381134919*t^2-\ 1523605662628367703948593144868133524552560729743114324293198087537230*t+7)/(t-\ 1)/(t^2-1764380986686440298536082635279244499396706231285168468374854076403714* t+1) 4*(1422585493543375697524163601998739994283972993193362251429140530487749*t^2-\ 2359099946147106367692491939198130830043542996269271273671474177286602*t+5)/(t-\ 1)/(t^2-1764380986686440298536082635279244499396706231285168468374854076403714* t+1) Then for all i>=0 we have 3 3 3 8 a(i) + 51 b(i) + 51 c(i) = -110592 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 232, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (192649945605865298058996107152238954599099 t / ----- i = 0 / + 276819724713637908731191157615487529460578 t - 29) / ((t - 1) / 2 (t - 39112028727232147833895072667626260962882 t + 1)) infinity ----- \ i 2 ) b(i) t = - 6 (37679666867485547911037242061739382234733 t / ----- i = 0 / - 33251495924802922895931364675604927054962 t + 5) / ((t - 1) / 2 (t - 39112028727232147833895072667626260962882 t + 1)) infinity ----- \ i 2 ) c(i) t = 32 (6837755998023982098815949741349437288589 t / ----- i = 0 / - 7668038049776974289148301751249647634798 t + 1) / ((t - 1) / 2 (t - 39112028727232147833895072667626260962882 t + 1)) In Maple notation, these generating functions are (192649945605865298058996107152238954599099*t^2+ 276819724713637908731191157615487529460578*t-29)/(t-1)/(t^2-\ 39112028727232147833895072667626260962882*t+1) -6*(37679666867485547911037242061739382234733*t^2-\ 33251495924802922895931364675604927054962*t+5)/(t-1)/(t^2-\ 39112028727232147833895072667626260962882*t+1) 32*(6837755998023982098815949741349437288589*t^2-\ 7668038049776974289148301751249647634798*t+1)/(t-1)/(t^2-\ 39112028727232147833895072667626260962882*t+1) Then for all i>=0 we have 3 3 3 8 a(i) + 53 b(i) + 53 c(i) = -110592 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 233, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 30 (571218282753456460043978046286170240470904519059 t / ----- i = 0 / + 709882998729698709075183922203831435997242380942 t - 1) / ((t - 1) / 2 (t - 2829221374126017775786532408573321710023907560002 t + 1)) infinity ----- \ i 2 ) b(i) t = - 16 (769650979583425194990941451926043676248779333326 t / ----- i = 0 / - 391946981077184619267878181905715595772825678327 t + 1) / ((t - 1) / 2 (t - 2829221374126017775786532408573321710023907560002 t + 1)) infinity ----- \ i 2 ) c(i) t = 22 (477753112029076248025376838775949911845393890401 t / ----- i = 0 / - 752446929124523939460331944245279424918814730402 t + 1) / ((t - 1) / 2 (t - 2829221374126017775786532408573321710023907560002 t + 1)) In Maple notation, these generating functions are 30*(571218282753456460043978046286170240470904519059*t^2+ 709882998729698709075183922203831435997242380942*t-1)/(t-1)/(t^2-\ 2829221374126017775786532408573321710023907560002*t+1) -16*(769650979583425194990941451926043676248779333326*t^2-\ 391946981077184619267878181905715595772825678327*t+1)/(t-1)/(t^2-\ 2829221374126017775786532408573321710023907560002*t+1) 22*(477753112029076248025376838775949911845393890401*t^2-\ 752446929124523939460331944245279424918814730402*t+1)/(t-1)/(t^2-\ 2829221374126017775786532408573321710023907560002*t+1) Then for all i>=0 we have 3 3 3 8 a(i) + 57 b(i) + 57 c(i) = -157464 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 234, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 2 / ----- i = 0 2 (1949311402855681465823325251 t + 145990364812460127718295141834 t - 13) / 2 / ((t - 1) (t - 554992631482309011968823124994 t + 1)) / infinity ----- \ i ) b(i) t = / ----- i = 0 2 8 (264524756240471495595187465 t + 11553141686994815036863980022 t + 1) - ------------------------------------------------------------------------ 2 (t - 1) (t - 554992631482309011968823124994 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 2 (624918713216178989975566471 t - 47895584486157325119812236430 t + 7) ------------------------------------------------------------------------ 2 (t - 1) (t - 554992631482309011968823124994 t + 1) In Maple notation, these generating functions are 2*(1949311402855681465823325251*t^2+145990364812460127718295141834*t-13)/(t-1)/ (t^2-554992631482309011968823124994*t+1) -8*(264524756240471495595187465*t^2+11553141686994815036863980022*t+1)/(t-1)/(t ^2-554992631482309011968823124994*t+1) 2*(624918713216178989975566471*t^2-47895584486157325119812236430*t+7)/(t-1)/(t^ 2-554992631482309011968823124994*t+1) Then for all i>=0 we have 3 3 3 8 a(i) + 63 b(i) + 63 c(i) = -8 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 235, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (28869708517780821870815097184416355183 t / ----- i = 0 / + 35357884874193786289260785374006684834 t - 17) / ((t - 1) / 2 (t - 7689900112442742995069326300293120002 t + 1)) infinity ----- \ i 2 ) b(i) t = - 4 (3783211703293084775398849789112860801 t / ----- i = 0 / + 472833641958244680991720741866979198 t + 1) / ((t - 1) / 2 (t - 7689900112442742995069326300293120002 t + 1)) infinity ----- \ i 2 ) c(i) t = 10 (988380890084855330690174512292119681 t / ----- i = 0 / - 2690799028185387113246402724684055682 t + 1) / ((t - 1) / 2 (t - 7689900112442742995069326300293120002 t + 1)) In Maple notation, these generating functions are (28869708517780821870815097184416355183*t^2+ 35357884874193786289260785374006684834*t-17)/(t-1)/(t^2-\ 7689900112442742995069326300293120002*t+1) -4*(3783211703293084775398849789112860801*t^2+ 472833641958244680991720741866979198*t+1)/(t-1)/(t^2-\ 7689900112442742995069326300293120002*t+1) 10*(988380890084855330690174512292119681*t^2-\ 2690799028185387113246402724684055682*t+1)/(t-1)/(t^2-\ 7689900112442742995069326300293120002*t+1) Then for all i>=0 we have 3 3 3 8 a(i) + 77 b(i) + 77 c(i) = -32768 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 236, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (55391 t + 3731534 t - 13) ) a(i) t = ----------------------------- / 2 ----- (t - 1) (t - 15100994 t + 1) i = 0 infinity ----- 2 \ i 16 (4870 t + 47617 t + 1) ) b(i) t = - ----------------------------- / 2 ----- (t - 1) (t - 15100994 t + 1) i = 0 infinity ----- 2 \ i 18 (3873 t - 50530 t + 1) ) c(i) t = ----------------------------- / 2 ----- (t - 1) (t - 15100994 t + 1) i = 0 In Maple notation, these generating functions are 2*(55391*t^2+3731534*t-13)/(t-1)/(t^2-15100994*t+1) -16*(4870*t^2+47617*t+1)/(t-1)/(t^2-15100994*t+1) 18*(3873*t^2-50530*t+1)/(t-1)/(t^2-15100994*t+1) Then for all i>=0 we have 3 3 3 8 a(i) + 81 b(i) + 81 c(i) = -8 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 237, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (87708788801677232472178399667448431989534327957933219 t / ----- i = 0 / + 518347122688796309890678735645527950934167885346591610 t - 29) / ( / 2 (t - 1) (t - 117522146315109217345145340151994550775639646579920898 t + 1) ) infinity ----- \ i 2 ) b(i) t = - 8 (5603422057158289318276009729934204146818788204579809 t / ----- i = 0 / + 11524245006702919487630822354997737109720622171417630 t + 1) / ( / 2 (t - 1) (t - 117522146315109217345145340151994550775639646579920898 t + 1) ) infinity ----- \ i 2 ) c(i) t = 2 (15666858320811831698321085099163860280387896821555143 t / ----- i = 0 / - 84177526576256666921948413438891625306545538325544910 t + 7) / ( / 2 (t - 1) (t - 117522146315109217345145340151994550775639646579920898 t + 1) ) In Maple notation, these generating functions are (87708788801677232472178399667448431989534327957933219*t^2+ 518347122688796309890678735645527950934167885346591610*t-29)/(t-1)/(t^2-\ 117522146315109217345145340151994550775639646579920898*t+1) -8*(5603422057158289318276009729934204146818788204579809*t^2+ 11524245006702919487630822354997737109720622171417630*t+1)/(t-1)/(t^2-\ 117522146315109217345145340151994550775639646579920898*t+1) 2*(15666858320811831698321085099163860280387896821555143*t^2-\ 84177526576256666921948413438891625306545538325544910*t+7)/(t-1)/(t^2-\ 117522146315109217345145340151994550775639646579920898*t+1) Then for all i>=0 we have 3 3 3 8 a(i) + 91 b(i) + 91 c(i) = -8000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 238, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (2252113761860627692799702590314105357897730309281571 t / ----- i = 0 / + 28962420677853729930917794879880610053005551773841658 t - 29) / ( / 2 (t - 1) (t - 9371498578927636281018092183962412108010492072652802 t + 1)) infinity ----- \ i 2 ) b(i) t = - 5 (206499072567114176105687915772774864353851819576705 t / ----- i = 0 / + 1792210091165004116690336097346520862708233540858494 t + 1) / ((t - 1) / 2 (t - 9371498578927636281018092183962412108010492072652802 t + 1)) infinity ----- \ i 2 ) c(i) t = (517726502981713122174221843934935954249777884333453 t / ----- i = 0 / - 10511272321642304586154341909531414589560204686509466 t + 13) / ( / 2 (t - 1) (t - 9371498578927636281018092183962412108010492072652802 t + 1)) In Maple notation, these generating functions are (2252113761860627692799702590314105357897730309281571*t^2+ 28962420677853729930917794879880610053005551773841658*t-29)/(t-1)/(t^2-\ 9371498578927636281018092183962412108010492072652802*t+1) -5*(206499072567114176105687915772774864353851819576705*t^2+ 1792210091165004116690336097346520862708233540858494*t+1)/(t-1)/(t^2-\ 9371498578927636281018092183962412108010492072652802*t+1) (517726502981713122174221843934935954249777884333453*t^2-\ 10511272321642304586154341909531414589560204686509466*t+13)/(t-1)/(t^2-\ 9371498578927636281018092183962412108010492072652802*t+1) Then for all i>=0 we have 3 3 3 8 a(i) + 95 b(i) + 95 c(i) = -1728 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 239, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 5 / ----- i = 0 2 (245335384681349830387344773779 t + 1919548978186027218634759436914 t - 5) / 2 / ((t - 1) (t - 2377262259224619734210981522498 t + 1)) / infinity ----- \ i ) b(i) t = / ----- i = 0 2 548467469203579588141981280699 t + 3068807668752037759591154868802 t + 3 - ------------------------------------------------------------------------- 2 (t - 1) (t - 2377262259224619734210981522498 t + 1) infinity ----- \ i ) c(i) t = ( / ----- i = 0 2 251091245347397975551260342787 t - 3868366383303015323284396492302 t + 11) / 2 / ((t - 1) (t - 2377262259224619734210981522498 t + 1)) / In Maple notation, these generating functions are 5*(245335384681349830387344773779*t^2+1919548978186027218634759436914*t-5)/(t-1 )/(t^2-2377262259224619734210981522498*t+1) -(548467469203579588141981280699*t^2+3068807668752037759591154868802*t+3)/(t-1) /(t^2-2377262259224619734210981522498*t+1) (251091245347397975551260342787*t^2-3868366383303015323284396492302*t+11)/(t-1) /(t^2-2377262259224619734210981522498*t+1) Then for all i>=0 we have 3 3 3 8 a(i) + 99 b(i) + 99 c(i) = -4096 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 240, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 1756771 t + 775152058 t - 29 ) a(i) t = ------------------------------ / 2 ----- (t - 1) (t - 881971202 t + 1) i = 0 infinity ----- 2 \ i 1696321 t + 744799678 t + 1 ) b(i) t = - ------------------------------ / 2 ----- (t - 1) (t - 881971202 t + 1) i = 0 infinity ----- 2 \ i 4 (28807 t - 186652814 t + 7) ) c(i) t = ------------------------------ / 2 ----- (t - 1) (t - 881971202 t + 1) i = 0 In Maple notation, these generating functions are (1756771*t^2+775152058*t-29)/(t-1)/(t^2-881971202*t+1) -(1696321*t^2+744799678*t+1)/(t-1)/(t^2-881971202*t+1) 4*(28807*t^2-186652814*t+7)/(t-1)/(t^2-881971202*t+1) Then for all i>=0 we have 3 3 3 9 a(i) + 10 b(i) + 10 c(i) = -9 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 241, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 10 (26914928482000734455543 t + 677293786149228542731658 t - 1) ---------------------------------------------------------------- 2 (t - 1) (t - 13825485377045766625593602 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 8 (38127002885359452099871 t + 317570256035516560356928 t + 1) - --------------------------------------------------------------- 2 (t - 1) (t - 13825485377045766625593602 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 231611672677419068283851 t - 3077189744044427167938262 t + 11 -------------------------------------------------------------- 2 (t - 1) (t - 13825485377045766625593602 t + 1) In Maple notation, these generating functions are 10*(26914928482000734455543*t^2+677293786149228542731658*t-1)/(t-1)/(t^2-\ 13825485377045766625593602*t+1) -8*(38127002885359452099871*t^2+317570256035516560356928*t+1)/(t-1)/(t^2-\ 13825485377045766625593602*t+1) (231611672677419068283851*t^2-3077189744044427167938262*t+11)/(t-1)/(t^2-\ 13825485377045766625593602*t+1) Then for all i>=0 we have 3 3 3 9 a(i) + 11 b(i) + 11 c(i) = -9 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 242, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 23 (183753291628320422399 t + 653846114513254017602 t - 1) ) a(i) t = ----------------------------------------------------------- / 2 ----- (t - 1) (t - 2569888732962123720002 t + 1) i = 0 infinity ----- \ i ) b(i) t = / ----- i = 0 2 3 (1251758402892297595801 t + 3137686586254687444198 t + 1) - ------------------------------------------------------------ 2 (t - 1) (t - 2569888732962123720002 t + 1) infinity ----- 2 \ i 3 (547370784983735976607 t - 4936815774130721016614 t + 7) ) c(i) t = ----------------------------------------------------------- / 2 ----- (t - 1) (t - 2569888732962123720002 t + 1) i = 0 In Maple notation, these generating functions are 23*(183753291628320422399*t^2+653846114513254017602*t-1)/(t-1)/(t^2-\ 2569888732962123720002*t+1) -3*(1251758402892297595801*t^2+3137686586254687444198*t+1)/(t-1)/(t^2-\ 2569888732962123720002*t+1) 3*(547370784983735976607*t^2-4936815774130721016614*t+7)/(t-1)/(t^2-\ 2569888732962123720002*t+1) Then for all i>=0 we have 3 3 3 9 a(i) + 14 b(i) + 14 c(i) = -19773 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 243, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (3949215310643 t + 19766754834650 t - 13) ) a(i) t = -------------------------------------------- / 2 ----- (t - 1) (t - 9291462276098 t + 1) i = 0 infinity ----- 2 \ i 15 (520250211937 t + 649304480158 t + 1) ) b(i) t = - ----------------------------------------- / 2 ----- (t - 1) (t - 9291462276098 t + 1) i = 0 infinity ----- 2 \ i 24 (242881063489 t - 973852746050 t + 1) ) c(i) t = ----------------------------------------- / 2 ----- (t - 1) (t - 9291462276098 t + 1) i = 0 In Maple notation, these generating functions are 2*(3949215310643*t^2+19766754834650*t-13)/(t-1)/(t^2-9291462276098*t+1) -15*(520250211937*t^2+649304480158*t+1)/(t-1)/(t^2-9291462276098*t+1) 24*(242881063489*t^2-973852746050*t+1)/(t-1)/(t^2-9291462276098*t+1) Then for all i>=0 we have 3 3 3 9 a(i) + 16 b(i) + 16 c(i) = -9000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 244, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (44127254303241217563494254743540764251 t / ----- i = 0 / + 64955823298595777093569292409474166978 t - 29) / ((t - 1) / 2 (t - 6612712807832406320831596458350798402 t + 1)) infinity ----- \ i 2 ) b(i) t = - (35203209653149797758744892992681488681 t / ----- i = 0 / + 34484983136068606050811271004201026518 t + 1) / ((t - 1) / 2 (t - 6612712807832406320831596458350798402 t + 1)) infinity ----- \ i 2 ) c(i) t = 28 (510743786993750374708091492799025201 t / ----- i = 0 / - 2999607815180121939335097349830543602 t + 1) / ((t - 1) / 2 (t - 6612712807832406320831596458350798402 t + 1)) In Maple notation, these generating functions are (44127254303241217563494254743540764251*t^2+ 64955823298595777093569292409474166978*t-29)/(t-1)/(t^2-\ 6612712807832406320831596458350798402*t+1) -(35203209653149797758744892992681488681*t^2+ 34484983136068606050811271004201026518*t+1)/(t-1)/(t^2-\ 6612712807832406320831596458350798402*t+1) 28*(510743786993750374708091492799025201*t^2-\ 2999607815180121939335097349830543602*t+1)/(t-1)/(t^2-\ 6612712807832406320831596458350798402*t+1) Then for all i>=0 we have 3 3 3 9 a(i) + 19 b(i) + 19 c(i) = -197568 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 245, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 24 (499647754855797362006841522516191697037278829924 t / ----- i = 0 / + 31008545273558142466923475522301324279677437514389 t - 1) / ((t - 1) / 2 (t - 1506961685400471337644162841070889144016408237096514 t + 1)) infinity ----- \ i 2 ) b(i) t = - 2 (6351920898043600658967537198201681667064348508719 t / ----- i = 0 / + 61542828644428576147187176306193604156662494372070 t + 11) / ((t - 1) / 2 (t - 1506961685400471337644162841070889144016408237096514 t + 1)) infinity ----- \ i 2 ) c(i) t = (11264856262102504915355370811556731246661333987257 t / ----- i = 0 / - 147054355347046858527664797820347302894115019748882 t + 25) / ((t - 1) / 2 (t - 1506961685400471337644162841070889144016408237096514 t + 1)) In Maple notation, these generating functions are 24*(499647754855797362006841522516191697037278829924*t^2+ 31008545273558142466923475522301324279677437514389*t-1)/(t-1)/(t^2-\ 1506961685400471337644162841070889144016408237096514*t+1) -2*(6351920898043600658967537198201681667064348508719*t^2+ 61542828644428576147187176306193604156662494372070*t+11)/(t-1)/(t^2-\ 1506961685400471337644162841070889144016408237096514*t+1) (11264856262102504915355370811556731246661333987257*t^2-\ 147054355347046858527664797820347302894115019748882*t+25)/(t-1)/(t^2-\ 1506961685400471337644162841070889144016408237096514*t+1) Then for all i>=0 we have 3 3 3 9 a(i) + 25 b(i) + 25 c(i) = -9 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 246, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = (34877823348512239719328221305409479411108112468839446236\ / ----- i = 0 2 17894602416253853281479461491 t + 4733451326217511076645743861145175860\ / 2 859766685040357011484629547287795050649635333738 t - 29) / ((t - 1) (t / - 651145231203706659442860362141721609251629831092624810138421687891736\ 116560716808002 t + 1)) infinity ----- \ i ) b(i) t = - 18 (177100176223364386232699606970007317124730094238651\ / ----- i = 0 2 813951514426730239770593574012921 t - 636748778846541939426529632420945\ / 2 20674446188177355879282240971420066382547513665722 t + 1) / ((t - 1) (t / - 651145231203706659442860362141721609251629831092624810138421687891736\ 116560716808002 t + 1)) infinity ----- \ i ) c(i) t = 27 (96537263563408208279004539643332359928148388462286736\ / ----- i = 0 2 315713972126232354140892061321 t - 172154129122548336472368968795274224\ / 2 228337659169817359428562942333014612838265626122 t + 1) / ((t - 1) (t - / 651145231203706659442860362141721609251629831092624810138421687891736116\ 560716808002 t + 1)) In Maple notation, these generating functions are (348778233485122397193282213054094794111081124688394462361789460241625385328147\ 9461491*t^2+4733451326217511076645743861145175860859766685040357011484629547287\ 795050649635333738*t-29)/(t-1)/(t^2-6511452312037066594428603621417216092516298\ 31092624810138421687891736116560716808002*t+1) -18*(17710017622336438623269960697000731712473009423865181395151442673023977059\ 3574012921*t^2-6367487788465419394265296324209452067444618817735587928224097142\ 0066382547513665722*t+1)/(t-1)/(t^2-6511452312037066594428603621417216092516298\ 31092624810138421687891736116560716808002*t+1) 27*(965372635634082082790045396433323599281483884622867363157139721262323541408\ 92061321*t^2-172154129122548336472368968795274224228337659169817359428562942333\ 014612838265626122*t+1)/(t-1)/(t^2-65114523120370665944286036214172160925162983\ 1092624810138421687891736116560716808002*t+1) Then for all i>=0 we have 3 3 3 9 a(i) + 26 b(i) + 26 c(i) = -140625 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 247, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 30 (29999877152485933440550648116883595483414107840132310\ / ----- i = 0 2 53372761879747179982399 t + 2339641015562621521101494305645331885720202\ / 2 87378433593654226993863803350823362 t - 1) / ((t - 1) (t - 1418460883\ / 4678536726591160520624420254498326482731816940808685638612637747920898 t + 1)) infinity ----- \ i ) b(i) t = - 4 (2357983148910269998886289802261136749170259867529331\ / ----- i = 0 2 6460640409467854604308711 t + 23400321100473430513473341708115153611445\ / 2 6805690898881305932312035199673982738 t + 7) / ((t - 1) (t - 14184608\ / 834678536726591160520624420254498326482731816940808685638612637747920898 t + 1)) infinity ----- \ i ) c(i) t = (85609684202463270892065920056511522890980492425005820848\ / ----- i = 0 2 898780801184668898847 t - 111594185417781129138645118047156313731561810\ / 2 9889774611915189666813401782064702 t + 31) / ((t - 1) (t - 1418460883\ / 4678536726591160520624420254498326482731816940808685638612637747920898 t + 1)) In Maple notation, these generating functions are 30*( 2999987715248593344055064811688359548341410784013231053372761879747179982399*t^ 2+ 233964101556262152110149430564533188572020287378433593654226993863803350823362* t-1)/(t-1)/(t^2-141846088346785367265911605206244202544983264827318169408086856\ 38612637747920898*t+1) -4*( 23579831489102699988862898022611367491702598675293316460640409467854604308711*t ^2+ 234003211004734305134733417081151536114456805690898881305932312035199673982738* t+7)/(t-1)/(t^2-141846088346785367265911605206244202544983264827318169408086856\ 38612637747920898*t+1) (85609684202463270892065920056511522890980492425005820848898780801184668898847* t^2-111594185417781129138645118047156313731561810988977461191518966681340178206\ 4702*t+31)/(t-1)/(t^2-141846088346785367265911605206244202544983264827318169408\ 08685638612637747920898*t+1) Then for all i>=0 we have 3 3 3 9 a(i) + 31 b(i) + 31 c(i) = -9 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 248, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 10 (12747083702603642562210108197087642111 t / ----- i = 0 / + 40867884523379905731937356153370092290 t - 1) / ((t - 1) / 2 (t - 155738717227856973616333110732281990402 t + 1)) infinity ----- \ i 2 ) b(i) t = - (86124473415516264445783098599729207761 t / ----- i = 0 / + 189609648889541983924118146631196283438 t + 1) / ((t - 1) / 2 (t - 155738717227856973616333110732281990402 t + 1)) infinity ----- \ i 2 ) c(i) t = (38322909530752604837495192860650549847 t / ----- i = 0 / - 314057031835810853207396438091576041054 t + 7) / ((t - 1) / 2 (t - 155738717227856973616333110732281990402 t + 1)) In Maple notation, these generating functions are 10*(12747083702603642562210108197087642111*t^2+ 40867884523379905731937356153370092290*t-1)/(t-1)/(t^2-\ 155738717227856973616333110732281990402*t+1) -(86124473415516264445783098599729207761*t^2+ 189609648889541983924118146631196283438*t+1)/(t-1)/(t^2-\ 155738717227856973616333110732281990402*t+1) (38322909530752604837495192860650549847*t^2-\ 314057031835810853207396438091576041054*t+7)/(t-1)/(t^2-\ 155738717227856973616333110732281990402*t+1) Then for all i>=0 we have 3 3 3 9 a(i) + 32 b(i) + 32 c(i) = -1944 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 249, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 26 (19568865540900097834259259932576779153993474499014961\ / ----- i = 0 2 6520786771308904980380096079 t + 15887374652092504552974855216154449415\ / 2 23122762029199294927343423526201151832396722 t - 1) / ((t - 1) (t - 1\ / 026472597499412685708933117174010711143781163382855500019922816549715204\ 8078572802 t + 1)) infinity ----- \ i ) b(i) t = - 5 (6776885093201569968250246541244329926207688903702191\ / ----- i = 0 2 28492596119402166090858342225 t + 3858060441363168372516975834760004229\ / 2 184242459740304813833705423763362467570601134 t + 1) / ((t - 1) (t - / 102647259749941268570893311717401071114378116338285550001992281654971520\ 48078572802 t + 1)) infinity ----- \ i ) c(i) t = (15927113557887760063930970650445311113256197331179579849\ / ----- i = 0 2 78113754411467104921417697 t - 2427145610920540285310309950946671722035\ / 2 0676483670577696609621470239109897066134514 t + 17) / ((t - 1) (t - 1\ / 026472597499412685708933117174010711143781163382855500019922816549715204\ 8078572802 t + 1)) In Maple notation, these generating functions are 26*(195688655409000978342592599325767791539934744990149616520786771308904980380\ 096079*t^2+15887374652092504552974855216154449415231227620291992949273434235262\ 01151832396722*t-1)/(t-1)/(t^2-102647259749941268570893311717401071114378116338\ 28555000199228165497152048078572802*t+1) -5*(677688509320156996825024654124432992620768890370219128492596119402166090858\ 342225*t^2+38580604413631683725169758347600042291842424597403048138337054237633\ 62467570601134*t+1)/(t-1)/(t^2-102647259749941268570893311717401071114378116338\ 28555000199228165497152048078572802*t+1) (159271135578877600639309706504453111132561973311795798497811375441146710492141\ 7697*t^2-2427145610920540285310309950946671722035067648367057769660962147023910\ 9897066134514*t+17)/(t-1)/(t^2-102647259749941268570893311717401071114378116338\ 28555000199228165497152048078572802*t+1) Then for all i>=0 we have 3 3 3 9 a(i) + 34 b(i) + 34 c(i) = -4608 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 250, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 27 (7343167 t + 807968706 t - 1) ) a(i) t = --------------------------------- / 2 ----- (t - 1) (t - 34829263874 t + 1) i = 0 infinity ----- 2 \ i 125160773 t + 12055414454 t + 5 ) b(i) t = - -------------------------------- / 2 ----- (t - 1) (t - 34829263874 t + 1) i = 0 infinity ----- 2 \ i 40189841 t - 12220765090 t + 17 ) c(i) t = -------------------------------- / 2 ----- (t - 1) (t - 34829263874 t + 1) i = 0 In Maple notation, these generating functions are 27*(7343167*t^2+807968706*t-1)/(t-1)/(t^2-34829263874*t+1) -(125160773*t^2+12055414454*t+5)/(t-1)/(t^2-34829263874*t+1) (40189841*t^2-12220765090*t+17)/(t-1)/(t^2-34829263874*t+1) Then for all i>=0 we have 3 3 3 9 a(i) + 37 b(i) + 37 c(i) = -9 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 251, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 30 (189037864716294600277549379598351 t / ----- i = 0 / + 1760317673624467347649023546238450 t - 1) / ((t - 1) / 2 (t - 13253086030147907529085206839942402 t + 1)) infinity ----- \ i 2 ) b(i) t = - (3683483636378533066803961615231927 t / ----- i = 0 / + 22291046004369801460113750357606466 t + 7) / ((t - 1) / 2 (t - 13253086030147907529085206839942402 t + 1)) infinity ----- \ i 2 ) c(i) t = (1892598602224163169437704334826499 t / ----- i = 0 / - 27867128242972497696355416307664918 t + 19) / ((t - 1) / 2 (t - 13253086030147907529085206839942402 t + 1)) In Maple notation, these generating functions are 30*(189037864716294600277549379598351*t^2+1760317673624467347649023546238450*t-\ 1)/(t-1)/(t^2-13253086030147907529085206839942402*t+1) -(3683483636378533066803961615231927*t^2+22291046004369801460113750357606466*t+ 7)/(t-1)/(t^2-13253086030147907529085206839942402*t+1) (1892598602224163169437704334826499*t^2-27867128242972497696355416307664918*t+ 19)/(t-1)/(t^2-13253086030147907529085206839942402*t+1) Then for all i>=0 we have 3 3 3 9 a(i) + 38 b(i) + 38 c(i) = -4608 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 252, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 8 (197456321962859 t + 1958086460228054 t - 1) ) a(i) t = ----------------------------------------------- / 2 ----- (t - 1) (t - 15780199990378754 t + 1) i = 0 infinity ----- 2 \ i 2 (507417640593289 t + 3152938027278070 t + 1) ) b(i) t = - ----------------------------------------------- / 2 ----- (t - 1) (t - 15780199990378754 t + 1) i = 0 infinity ----- 2 \ i 540940108475717 t - 7861651444218442 t + 5 ) c(i) t = ------------------------------------------- / 2 ----- (t - 1) (t - 15780199990378754 t + 1) i = 0 In Maple notation, these generating functions are 8*(197456321962859*t^2+1958086460228054*t-1)/(t-1)/(t^2-15780199990378754*t+1) -2*(507417640593289*t^2+3152938027278070*t+1)/(t-1)/(t^2-15780199990378754*t+1) (540940108475717*t^2-7861651444218442*t+5)/(t-1)/(t^2-15780199990378754*t+1) Then for all i>=0 we have 3 3 3 9 a(i) + 40 b(i) + 40 c(i) = -72 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 253, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 3 ( / ----- i = 0 2 492215705482771094886309531471987993075896747275290766298742336337 t + 543456931579058286365174396608710891428375524669658449257689145270 t - 7 / 2 ) / ((t - 1) (t / - 310286290952119848650426009537758270553635093896374606734982584898 t + 1 )) infinity ----- \ i ) b(i) t = - ( / ----- i = 0 2 1530341342036801317164582420759120043561348312600860119871151077211 t - 1189631205565049422648863933868976309491146409170530615674726218350 t / 2 + 19) / ((t - 1) (t / - 310286290952119848650426009537758270553635093896374606734982584898 t + 1 )) infinity ----- \ i ) c(i) t = 2 ( / ----- i = 0 2 711146996026389196948427969120439388394295245014117658756445282179 t - 881502064262265144206287212565511255429396196729282410854657711630 t / 2 + 11) / ((t - 1) (t / - 310286290952119848650426009537758270553635093896374606734982584898 t + 1 )) In Maple notation, these generating functions are 3*(492215705482771094886309531471987993075896747275290766298742336337*t^2+ 543456931579058286365174396608710891428375524669658449257689145270*t-7)/(t-1)/( t^2-310286290952119848650426009537758270553635093896374606734982584898*t+1) -(1530341342036801317164582420759120043561348312600860119871151077211*t^2-\ 1189631205565049422648863933868976309491146409170530615674726218350*t+19)/(t-1) /(t^2-310286290952119848650426009537758270553635093896374606734982584898*t+1) 2*(711146996026389196948427969120439388394295245014117658756445282179*t^2-\ 881502064262265144206287212565511255429396196729282410854657711630*t+11)/(t-1)/ (t^2-310286290952119848650426009537758270553635093896374606734982584898*t+1) Then for all i>=0 we have 3 3 3 9 a(i) + 41 b(i) + 41 c(i) = -72000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 254, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 24 (407377534625388630456804498011187202515613588739 t / ----- i = 0 / + 549364315689446673643309400224698303287185298462 t - 1) / ((t - 1) / 2 (t - 1951545763390839462974554208336489783988349267202 t + 1)) infinity ----- \ i 2 ) b(i) t = - 5 (1221606938151831017174498550018678565342539511993 t / ----- i = 0 / + 497414223643504169360534305835165627362091544646 t + 1) / ((t - 1) / 2 (t - 1951545763390839462974554208336489783988349267202 t + 1)) infinity ----- \ i 2 ) c(i) t = 17 (209264534274692082325543441275030889647426309721 t / ----- i = 0 / - 714858993626261254835847222408514475737023679322 t + 1) / ((t - 1) / 2 (t - 1951545763390839462974554208336489783988349267202 t + 1)) In Maple notation, these generating functions are 24*(407377534625388630456804498011187202515613588739*t^2+ 549364315689446673643309400224698303287185298462*t-1)/(t-1)/(t^2-\ 1951545763390839462974554208336489783988349267202*t+1) -5*(1221606938151831017174498550018678565342539511993*t^2+ 497414223643504169360534305835165627362091544646*t+1)/(t-1)/(t^2-\ 1951545763390839462974554208336489783988349267202*t+1) 17*(209264534274692082325543441275030889647426309721*t^2-\ 714858993626261254835847222408514475737023679322*t+1)/(t-1)/(t^2-\ 1951545763390839462974554208336489783988349267202*t+1) Then for all i>=0 we have 3 3 3 9 a(i) + 46 b(i) + 46 c(i) = -95832 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 255, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 24 (18672540717857296535090979436923350000875491224259105\ / ----- i = 0 2 037192673297011079598088499 t + 203540958268720706541188864816537685457\ / 2 60593386235834726351697309941178883911502 t - 1) / ((t - 1) (t - 8136\ / 399136915972197097821558973476898732803761442958282459504748786938996800\ 0002 t + 1)) infinity ----- \ i ) b(i) t = - 2 (2311836329695158088805856748686693697179356329607822\ / ----- i = 0 2 48136985700425014389759046011 t - 1863749455456193447655824449653222867\ / 2 63236522921679711552558822976272099767046022 t + 11) / ((t - 1) (t - / 813639913691597219709782155897347689873280376144295828245950474878693899\ 68000002 t + 1)) infinity ----- \ i ) c(i) t = 25 (17350500908467030369573193972933140045466309898014362\ / ----- i = 0 2 350807475202184302047904641 t - 209351959023787474987734523652009066818\ / 2 42238701142565277561625398083685247264642 t + 1) / ((t - 1) (t - 8136\ / 399136915972197097821558973476898732803761442958282459504748786938996800\ 0002 t + 1)) In Maple notation, these generating functions are 24*(186725407178572965350909794369233500008754912242591050371926732970110795980\ 88499*t^2+203540958268720706541188864816537685457605933862358347263516973099411\ 78883911502*t-1)/(t-1)/(t^2-813639913691597219709782155897347689873280376144295\ 82824595047487869389968000002*t+1) -2*(231183632969515808880585674868669369717935632960782248136985700425014389759\ 046011*t^2-18637494554561934476558244496532228676323652292167971155255882297627\ 2099767046022*t+11)/(t-1)/(t^2-813639913691597219709782155897347689873280376144\ 29582824595047487869389968000002*t+1) 25*(173505009084670303695731939729331400454663098980143623508074752021843020479\ 04641*t^2-209351959023787474987734523652009066818422387011425652775616253980836\ 85247264642*t+1)/(t-1)/(t^2-813639913691597219709782155897347689873280376144295\ 82824595047487869389968000002*t+1) Then for all i>=0 we have 3 3 3 9 a(i) + 47 b(i) + 47 c(i) = -109503 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 256, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 4 (995299723134604361453899427638021222400852633 t / ----- i = 0 / + 8245244174968948403729604940914712816221259118 t - 7) / ((t - 1) / 2 (t - 8511027274569061757405859286824886614520366082 t + 1)) infinity ----- \ i 2 ) b(i) t = - 6 (366241289714925651363177314147308280763072385 t / ----- i = 0 / + 1822308580888547371969757931036233991542164606 t + 1) / ((t - 1) / 2 (t - 8511027274569061757405859286824886614520366082 t + 1)) infinity ----- \ i 2 ) c(i) t = 3 (400716005051649848908388152415276154059193893 t / ----- i = 0 / - 4777815746258595895574258642782360698669667882 t + 5) / ((t - 1) / 2 (t - 8511027274569061757405859286824886614520366082 t + 1)) In Maple notation, these generating functions are 4*(995299723134604361453899427638021222400852633*t^2+ 8245244174968948403729604940914712816221259118*t-7)/(t-1)/(t^2-\ 8511027274569061757405859286824886614520366082*t+1) -6*(366241289714925651363177314147308280763072385*t^2+ 1822308580888547371969757931036233991542164606*t+1)/(t-1)/(t^2-\ 8511027274569061757405859286824886614520366082*t+1) 3*(400716005051649848908388152415276154059193893*t^2-\ 4777815746258595895574258642782360698669667882*t+5)/(t-1)/(t^2-\ 8511027274569061757405859286824886614520366082*t+1) Then for all i>=0 we have 3 3 3 9 a(i) + 64 b(i) + 64 c(i) = -4608 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 257, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 30 (8870548321002413491158212923862714189824516767 t / ----- i = 0 / + 165902722019976946627919445457484112073828968034 t - 1) / ((t - 1) / 2 (t - 2541618066992547304782519167647382659901943897602 t + 1)) infinity ----- \ i 2 ) b(i) t = - (155846672781064370762429608422557970712645818491 t / ----- i = 0 / + 1203830125295368278299547428815377508185946546298 t + 11) / ((t - 1) / 2 (t - 2541618066992547304782519167647382659901943897602 t + 1)) infinity ----- \ i 2 ) c(i) t = (108884946375757475809239069413873013237104259137 t / ----- i = 0 / - 1468561744452190124871216106651808492135696623954 t + 17) / ((t - 1) / 2 (t - 2541618066992547304782519167647382659901943897602 t + 1)) In Maple notation, these generating functions are 30*(8870548321002413491158212923862714189824516767*t^2+ 165902722019976946627919445457484112073828968034*t-1)/(t-1)/(t^2-\ 2541618066992547304782519167647382659901943897602*t+1) -(155846672781064370762429608422557970712645818491*t^2+ 1203830125295368278299547428815377508185946546298*t+11)/(t-1)/(t^2-\ 2541618066992547304782519167647382659901943897602*t+1) (108884946375757475809239069413873013237104259137*t^2-\ 1468561744452190124871216106651808492135696623954*t+17)/(t-1)/(t^2-\ 2541618066992547304782519167647382659901943897602*t+1) Then for all i>=0 we have 3 3 3 9 a(i) + 68 b(i) + 68 c(i) = -576 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 258, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 9 ( / ----- i = 0 2 140995321357507780913031197050174280861235313005882002290397 t / + 256471103687795381635782122811765121931297150619492353812006 t - 3) / / ((t - 1) 2 (t - 266723977145293938118040966761572949621351216491471951340802 t + 1)) infinity ----- \ i ) b(i) t = - ( / ----- i = 0 2 657204903695002560523886161326962685615353189710807104674641 t / + 799572491267420795424253155814082184348227333079026508189358 t + 1) / / ((t - 1) 2 (t - 266723977145293938118040966761572949621351216491471951340802 t + 1)) infinity ----- \ i ) c(i) t = 16 ( / ----- i = 0 2 17282346001858222003668870580718257955626115287182856155661 t / - 108330933187009681750427577902033562328349897961547456959662 t + 1) / / ((t - 1) 2 (t - 266723977145293938118040966761572949621351216491471951340802 t + 1)) In Maple notation, these generating functions are 9*(140995321357507780913031197050174280861235313005882002290397*t^2+ 256471103687795381635782122811765121931297150619492353812006*t-3)/(t-1)/(t^2-\ 266723977145293938118040966761572949621351216491471951340802*t+1) -(657204903695002560523886161326962685615353189710807104674641*t^2+ 799572491267420795424253155814082184348227333079026508189358*t+1)/(t-1)/(t^2-\ 266723977145293938118040966761572949621351216491471951340802*t+1) 16*(17282346001858222003668870580718257955626115287182856155661*t^2-\ 108330933187009681750427577902033562328349897961547456959662*t+1)/(t-1)/(t^2-\ 266723977145293938118040966761572949621351216491471951340802*t+1) Then for all i>=0 we have 3 3 3 9 a(i) + 70 b(i) + 70 c(i) = -109503 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 259, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 20 (26914928482000734455543 t + 677293786149228542731658 t - 1) ---------------------------------------------------------------- 2 (t - 1) (t - 13825485377045766625593602 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 8 (38127002885359452099871 t + 317570256035516560356928 t + 1) - --------------------------------------------------------------- 2 (t - 1) (t - 13825485377045766625593602 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 231611672677419068283851 t - 3077189744044427167938262 t + 11 -------------------------------------------------------------- 2 (t - 1) (t - 13825485377045766625593602 t + 1) In Maple notation, these generating functions are 20*(26914928482000734455543*t^2+677293786149228542731658*t-1)/(t-1)/(t^2-\ 13825485377045766625593602*t+1) -8*(38127002885359452099871*t^2+317570256035516560356928*t+1)/(t-1)/(t^2-\ 13825485377045766625593602*t+1) (231611672677419068283851*t^2-3077189744044427167938262*t+11)/(t-1)/(t^2-\ 13825485377045766625593602*t+1) Then for all i>=0 we have 3 3 3 9 a(i) + 88 b(i) + 88 c(i) = -72 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 260, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 7 / ----- i = 0 2 (24941896087434883818757397999 t + 29156962745184387313420962002 t - 1) / 2 / ((t - 1) (t - 99945349368737297515380360002 t + 1)) / infinity ----- \ i ) b(i) t = / ----- i = 0 2 83806682082130413495345501001 t + 31726474068887012990323538998 t + 1 - ---------------------------------------------------------------------- 2 (t - 1) (t - 99945349368737297515380360002 t + 1) infinity ----- \ i ) c(i) t = 4 / ----- i = 0 2 (11598459487744521941802351001 t - 40481748525498878563219611002 t + 1) / 2 / ((t - 1) (t - 99945349368737297515380360002 t + 1)) / In Maple notation, these generating functions are 7*(24941896087434883818757397999*t^2+29156962745184387313420962002*t-1)/(t-1)/( t^2-99945349368737297515380360002*t+1) -(83806682082130413495345501001*t^2+31726474068887012990323538998*t+1)/(t-1)/(t ^2-99945349368737297515380360002*t+1) 4*(11598459487744521941802351001*t^2-40481748525498878563219611002*t+1)/(t-1)/( t^2-99945349368737297515380360002*t+1) Then for all i>=0 we have 3 3 3 9 a(i) + 98 b(i) + 98 c(i) = -3087 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 261, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 4 (88 t + 7069 t - 3) ) a(i) t = -------------------------- / 2 ----- (t - 1) (t - 37634 t + 1) i = 0 infinity ----- 2 \ i 323 t + 25156 t + 1 ) b(i) t = - -------------------------- / 2 ----- (t - 1) (t - 37634 t + 1) i = 0 infinity ----- 2 \ i 53 t - 25544 t + 11 ) c(i) t = -------------------------- / 2 ----- (t - 1) (t - 37634 t + 1) i = 0 In Maple notation, these generating functions are 4*(88*t^2+7069*t-3)/(t-1)/(t^2-37634*t+1) -(323*t^2+25156*t+1)/(t-1)/(t^2-37634*t+1) (53*t^2-25544*t+11)/(t-1)/(t^2-37634*t+1) Then for all i>=0 we have 3 3 3 10 a(i) + 13 b(i) + 13 c(i) = -10 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 262, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 5318560283 t + 56568444434 t - 13 ) a(i) t = ---------------------------------- / 2 ----- (t - 1) (t - 24097594754 t + 1) i = 0 infinity ----- 2 \ i 4499136433 t + 42053035246 t + 1 ) b(i) t = - --------------------------------- / 2 ----- (t - 1) (t - 24097594754 t + 1) i = 0 infinity ----- 2 \ i 1370571563 t - 47922743254 t + 11 ) c(i) t = ---------------------------------- / 2 ----- (t - 1) (t - 24097594754 t + 1) i = 0 In Maple notation, these generating functions are (5318560283*t^2+56568444434*t-13)/(t-1)/(t^2-24097594754*t+1) -(4499136433*t^2+42053035246*t+1)/(t-1)/(t^2-24097594754*t+1) (1370571563*t^2-47922743254*t+11)/(t-1)/(t^2-24097594754*t+1) Then for all i>=0 we have 3 3 3 10 a(i) + 17 b(i) + 17 c(i) = -640 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 263, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 4 (281954 t + 435623 t - 3) ) a(i) t = ---------------------------- / 2 ----- (t - 1) (t - 454274 t + 1) i = 0 infinity ----- 2 \ i 880751 t + 829528 t + 1 ) b(i) t = - --------------------------- / 2 ----- (t - 1) (t - 454274 t + 1) i = 0 infinity ----- 2 \ i 11 (35491 t - 190972 t + 1) ) c(i) t = ---------------------------- / 2 ----- (t - 1) (t - 454274 t + 1) i = 0 In Maple notation, these generating functions are 4*(281954*t^2+435623*t-3)/(t-1)/(t^2-454274*t+1) -(880751*t^2+829528*t+1)/(t-1)/(t^2-454274*t+1) 11*(35491*t^2-190972*t+1)/(t-1)/(t^2-454274*t+1) Then for all i>=0 we have 3 3 3 10 a(i) + 23 b(i) + 23 c(i) = -13310 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 264, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 27 (1083371277951453151627861078654669679 t / ----- i = 0 / + 4525299367895558501729239167566249522 t - 1) / ((t - 1) / 2 (t - 24396594077662969247847039522280046402 t + 1)) infinity ----- \ i 2 ) b(i) t = - (23931274253310387053871729961270831571 t / ----- i = 0 / + 33016576563333836742898293233001652418 t + 11) / ((t - 1) / 2 (t - 24396594077662969247847039522280046402 t + 1)) infinity ----- \ i 2 ) c(i) t = 3 (5477003853266775591123717754297449727 t / ----- i = 0 / - 24459620792148183523380392152388277734 t + 7) / ((t - 1) / 2 (t - 24396594077662969247847039522280046402 t + 1)) In Maple notation, these generating functions are 27*(1083371277951453151627861078654669679*t^2+ 4525299367895558501729239167566249522*t-1)/(t-1)/(t^2-\ 24396594077662969247847039522280046402*t+1) -(23931274253310387053871729961270831571*t^2+ 33016576563333836742898293233001652418*t+11)/(t-1)/(t^2-\ 24396594077662969247847039522280046402*t+1) 3*(5477003853266775591123717754297449727*t^2-\ 24459620792148183523380392152388277734*t+7)/(t-1)/(t^2-\ 24396594077662969247847039522280046402*t+1) Then for all i>=0 we have 3 3 3 10 a(i) + 27 b(i) + 27 c(i) = -17280 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 265, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 4 (2809 t + 4917 t - 4) ) a(i) t = ------------------------- / 2 ----- (t - 1) (t - 4354 t + 1) i = 0 infinity ----- 2 \ i 8329 t + 6748 t + 3 ) b(i) t = - ------------------------- / 2 ----- (t - 1) (t - 4354 t + 1) i = 0 infinity ----- 2 \ i 13 (343 t - 1504 t + 1) ) c(i) t = ------------------------- / 2 ----- (t - 1) (t - 4354 t + 1) i = 0 In Maple notation, these generating functions are 4*(2809*t^2+4917*t-4)/(t-1)/(t^2-4354*t+1) -(8329*t^2+6748*t+3)/(t-1)/(t^2-4354*t+1) 13*(343*t^2-1504*t+1)/(t-1)/(t^2-4354*t+1) Then for all i>=0 we have 3 3 3 10 a(i) + 29 b(i) + 29 c(i) = -21970 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 266, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 12 (4421311 t + 35337277 t - 2) ) a(i) t = -------------------------------- / 2 ----- (t - 1) (t - 126202754 t + 1) i = 0 infinity ----- 2 \ i 7 (5541151 t + 25807288 t + 1) ) b(i) t = - ------------------------------- / 2 ----- (t - 1) (t - 126202754 t + 1) i = 0 infinity ----- 2 \ i 21673307 t - 241112404 t + 17 ) c(i) t = ------------------------------ / 2 ----- (t - 1) (t - 126202754 t + 1) i = 0 In Maple notation, these generating functions are 12*(4421311*t^2+35337277*t-2)/(t-1)/(t^2-126202754*t+1) -7*(5541151*t^2+25807288*t+1)/(t-1)/(t^2-126202754*t+1) (21673307*t^2-241112404*t+17)/(t-1)/(t^2-126202754*t+1) Then for all i>=0 we have 3 3 3 10 a(i) + 31 b(i) + 31 c(i) = -3430 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 267, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 4 (9872 t + 66761 t - 7) ) a(i) t = -------------------------- / 2 ----- (t - 1) (t - 64514 t + 1) i = 0 infinity ----- 2 \ i 9 (3103 t + 10216 t + 1) ) b(i) t = - -------------------------- / 2 ----- (t - 1) (t - 64514 t + 1) i = 0 infinity ----- 2 \ i 17257 t - 137156 t + 19 ) c(i) t = -------------------------- / 2 ----- (t - 1) (t - 64514 t + 1) i = 0 In Maple notation, these generating functions are 4*(9872*t^2+66761*t-7)/(t-1)/(t^2-64514*t+1) -9*(3103*t^2+10216*t+1)/(t-1)/(t^2-64514*t+1) (17257*t^2-137156*t+19)/(t-1)/(t^2-64514*t+1) Then for all i>=0 we have 3 3 3 10 a(i) + 37 b(i) + 37 c(i) = -7290 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 268, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 4 (6431 t + 13193 t - 6) ) a(i) t = ------------------------- / 2 ----- (t - 1) (t - 8834 t + 1) i = 0 infinity ----- 2 \ i 17881 t + 9992 t + 7 ) b(i) t = - ------------------------- / 2 ----- (t - 1) (t - 8834 t + 1) i = 0 infinity ----- 2 \ i 17 (683 t - 2324 t + 1) ) c(i) t = ------------------------- / 2 ----- (t - 1) (t - 8834 t + 1) i = 0 In Maple notation, these generating functions are 4*(6431*t^2+13193*t-6)/(t-1)/(t^2-8834*t+1) -(17881*t^2+9992*t+7)/(t-1)/(t^2-8834*t+1) 17*(683*t^2-2324*t+1)/(t-1)/(t^2-8834*t+1) Then for all i>=0 we have 3 3 3 10 a(i) + 41 b(i) + 41 c(i) = -49130 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 269, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 4 (6594986 t + 14264627 t - 7) ) a(i) t = ------------------------------- / 2 ----- (t - 1) (t - 8491394 t + 1) i = 0 infinity ----- 2 \ i 9 (1994491 t + 898828 t + 1) ) b(i) t = - ----------------------------- / 2 ----- (t - 1) (t - 8491394 t + 1) i = 0 infinity ----- 2 \ i 19 (649351 t - 2019872 t + 1) ) c(i) t = ------------------------------ / 2 ----- (t - 1) (t - 8491394 t + 1) i = 0 In Maple notation, these generating functions are 4*(6594986*t^2+14264627*t-7)/(t-1)/(t^2-8491394*t+1) -9*(1994491*t^2+898828*t+1)/(t-1)/(t^2-8491394*t+1) 19*(649351*t^2-2019872*t+1)/(t-1)/(t^2-8491394*t+1) Then for all i>=0 we have 3 3 3 10 a(i) + 47 b(i) + 47 c(i) = -68590 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 270, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 26 (66182184485 t + 8152174767464 t - 1) ) a(i) t = ----------------------------------------- / 2 ----- (t - 1) (t - 317963462140898 t + 1) i = 0 infinity ----- 2 \ i 861928186837 t + 97590061237520 t + 3 ) b(i) t = - -------------------------------------- / 2 ----- (t - 1) (t - 317963462140898 t + 1) i = 0 infinity ----- 2 \ i 13 (17278327859 t - 7590508283580 t + 1) ) c(i) t = ----------------------------------------- / 2 ----- (t - 1) (t - 317963462140898 t + 1) i = 0 In Maple notation, these generating functions are 26*(66182184485*t^2+8152174767464*t-1)/(t-1)/(t^2-317963462140898*t+1) -(861928186837*t^2+97590061237520*t+3)/(t-1)/(t^2-317963462140898*t+1) 13*(17278327859*t^2-7590508283580*t+1)/(t-1)/(t^2-317963462140898*t+1) Then for all i>=0 we have 3 3 3 10 a(i) + 81 b(i) + 81 c(i) = -10 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 271, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 76481383784233 t + 453510592762270 t - 23 ) a(i) t = ------------------------------------------ / 2 ----- (t - 1) (t - 86749292044898 t + 1) i = 0 infinity ----- 2 \ i 36188338413909 t + 175551797494490 t + 1 ) b(i) t = - ----------------------------------------- / 2 ----- (t - 1) (t - 86749292044898 t + 1) i = 0 infinity ----- 2 \ i 13012161509599 t - 224752297418010 t + 11 ) c(i) t = ------------------------------------------ / 2 ----- (t - 1) (t - 86749292044898 t + 1) i = 0 In Maple notation, these generating functions are (76481383784233*t^2+453510592762270*t-23)/(t-1)/(t^2-86749292044898*t+1) -(36188338413909*t^2+175551797494490*t+1)/(t-1)/(t^2-86749292044898*t+1) (13012161509599*t^2-224752297418010*t+11)/(t-1)/(t^2-86749292044898*t+1) Then for all i>=0 we have 3 3 3 10 a(i) + 99 b(i) + 99 c(i) = -10000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 272, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 90931 t + 8489178 t - 13 ) a(i) t = ----------------------------- / 2 ----- (t - 1) (t - 11088898 t + 1) i = 0 infinity ----- 2 \ i 84001 t + 7643102 t + 1 ) b(i) t = - ----------------------------- / 2 ----- (t - 1) (t - 11088898 t + 1) i = 0 infinity ----- 2 \ i 4 (3139 t - 1934918 t + 3) ) c(i) t = ----------------------------- / 2 ----- (t - 1) (t - 11088898 t + 1) i = 0 In Maple notation, these generating functions are (90931*t^2+8489178*t-13)/(t-1)/(t^2-11088898*t+1) -(84001*t^2+7643102*t+1)/(t-1)/(t^2-11088898*t+1) 4*(3139*t^2-1934918*t+3)/(t-1)/(t^2-11088898*t+1) Then for all i>=0 we have 3 3 3 11 a(i) + 14 b(i) + 14 c(i) = -11 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 273, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 7264697 t + 239707862 t - 15 ) a(i) t = ------------------------------ / 2 ----- (t - 1) (t - 182844482 t + 1) i = 0 infinity ----- 2 \ i 2 (3159521 t + 95947486 t + 1) ) b(i) t = - ------------------------------- / 2 ----- (t - 1) (t - 182844482 t + 1) i = 0 infinity ----- 2 \ i 13 (124489 t - 15371722 t + 1) ) c(i) t = ------------------------------- / 2 ----- (t - 1) (t - 182844482 t + 1) i = 0 In Maple notation, these generating functions are (7264697*t^2+239707862*t-15)/(t-1)/(t^2-182844482*t+1) -2*(3159521*t^2+95947486*t+1)/(t-1)/(t^2-182844482*t+1) 13*(124489*t^2-15371722*t+1)/(t-1)/(t^2-182844482*t+1) Then for all i>=0 we have 3 3 3 11 a(i) + 17 b(i) + 17 c(i) = -88 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 274, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = (42831180737502396632358700874462910836650265194204142575\ / ----- i = 0 2 271090129736294770185 t + 642917052730267391982557069974819075619249850\ / 2 07834747391159537748635450870542 t - 23) / ((t - 1) (t - 110310781885\ / 49198629422339706825749129451853503953332737191023404236923632898 t + 1)) infinity ----- \ i ) b(i) t = - 13 (332641031659844262851435214019595258494235822066204\ / ----- i = 0 2 1829226724950039919458161 t - 136074155863458189241433197597074773184331540672413320340588687999987002738 / 2 t + 1) / ((t - 1) (t - 1103107818854919862942233970682574912945185350\ / 3953332737191023404236923632898 t + 1)) infinity ----- \ i ) c(i) t = 24 (13344018301093485240207247608411687422374748723662988\ / ----- i = 0 2 79394652610411405537385 t - 3062500583840798428626889188082227556939739\ / 2 324027347655041309752349702284074 t + 1) / ((t - 1) (t - 110310781885\ / 49198629422339706825749129451853503953332737191023404236923632898 t + 1)) In Maple notation, these generating functions are (42831180737502396632358700874462910836650265194204142575271090129736294770185* t^2+ 64291705273026739198255706997481907561924985007834747391159537748635450870542*t -23)/(t-1)/(t^2-\ 11031078188549198629422339706825749129451853503953332737191023404236923632898*t +1) -13*( 3326410316598442628514352140195952584942358220662041829226724950039919458161*t^ 2-136074155863458189241433197597074773184331540672413320340588687999987002738*t +1)/(t-1)/(t^2-\ 11031078188549198629422339706825749129451853503953332737191023404236923632898*t +1) 24*( 1334401830109348524020724760841168742237474872366298879394652610411405537385*t^ 2-3062500583840798428626889188082227556939739324027347655041309752349702284074* t+1)/(t-1)/(t^2-\ 11031078188549198629422339706825749129451853503953332737191023404236923632898*t +1) Then for all i>=0 we have 3 3 3 11 a(i) + 18 b(i) + 18 c(i) = -75449 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 275, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 316890286919771902178383 t + 6225122439618338927455234 t - 17 -------------------------------------------------------------- 2 (t - 1) (t - 3501859146778815026068802 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 3 (87682494833736510347641 t + 1475013270463097781204358 t + 1) - ---------------------------------------------------------------- 2 (t - 1) (t - 3501859146778815026068802 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 2 (44378913347667492422407 t - 2388422561292918929750414 t + 7) ---------------------------------------------------------------- 2 (t - 1) (t - 3501859146778815026068802 t + 1) In Maple notation, these generating functions are (316890286919771902178383*t^2+6225122439618338927455234*t-17)/(t-1)/(t^2-\ 3501859146778815026068802*t+1) -3*(87682494833736510347641*t^2+1475013270463097781204358*t+1)/(t-1)/(t^2-\ 3501859146778815026068802*t+1) 2*(44378913347667492422407*t^2-2388422561292918929750414*t+7)/(t-1)/(t^2-\ 3501859146778815026068802*t+1) Then for all i>=0 we have 3 3 3 11 a(i) + 20 b(i) + 20 c(i) = -297 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 276, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 19 (6142471 t + 87523578 t - 1) ) a(i) t = -------------------------------- / 2 ----- (t - 1) (t - 752843842 t + 1) i = 0 infinity ----- 2 \ i 4 (23333521 t + 263086766 t + 1) ) b(i) t = - --------------------------------- / 2 ----- (t - 1) (t - 752843842 t + 1) i = 0 infinity ----- 2 \ i 37517719 t - 1183198886 t + 15 ) c(i) t = ------------------------------- / 2 ----- (t - 1) (t - 752843842 t + 1) i = 0 In Maple notation, these generating functions are 19*(6142471*t^2+87523578*t-1)/(t-1)/(t^2-752843842*t+1) -4*(23333521*t^2+263086766*t+1)/(t-1)/(t^2-752843842*t+1) (37517719*t^2-1183198886*t+15)/(t-1)/(t^2-752843842*t+1) Then for all i>=0 we have 3 3 3 11 a(i) + 23 b(i) + 23 c(i) = -704 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 277, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (2850889 t + 63878434 t - 11) ) a(i) t = -------------------------------- / 2 ----- (t - 1) (t - 77193794 t + 1) i = 0 infinity ----- 2 \ i 6 (744277 t + 12640522 t + 1) ) b(i) t = - ------------------------------ / 2 ----- (t - 1) (t - 77193794 t + 1) i = 0 infinity ----- 2 \ i 1956881 t - 82265698 t + 17 ) c(i) t = ----------------------------- / 2 ----- (t - 1) (t - 77193794 t + 1) i = 0 In Maple notation, these generating functions are 2*(2850889*t^2+63878434*t-11)/(t-1)/(t^2-77193794*t+1) -6*(744277*t^2+12640522*t+1)/(t-1)/(t^2-77193794*t+1) (1956881*t^2-82265698*t+17)/(t-1)/(t^2-77193794*t+1) Then for all i>=0 we have 3 3 3 11 a(i) + 25 b(i) + 25 c(i) = -297 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 278, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 21 (12821867917775279 t + 146490407759016722 t - 1) ) a(i) t = ---------------------------------------------------- / 2 ----- (t - 1) (t - 1173330043385774402 t + 1) i = 0 infinity ----- 2 \ i 5 (41779505839193641 t + 347967755959100758 t + 1) ) b(i) t = - --------------------------------------------------- / 2 ----- (t - 1) (t - 1173330043385774402 t + 1) i = 0 infinity ----- 2 \ i 16 (5936260264637221 t - 127732279576604222 t + 1) ) c(i) t = --------------------------------------------------- / 2 ----- (t - 1) (t - 1173330043385774402 t + 1) i = 0 In Maple notation, these generating functions are 21*(12821867917775279*t^2+146490407759016722*t-1)/(t-1)/(t^2-\ 1173330043385774402*t+1) -5*(41779505839193641*t^2+347967755959100758*t+1)/(t-1)/(t^2-\ 1173330043385774402*t+1) 16*(5936260264637221*t^2-127732279576604222*t+1)/(t-1)/(t^2-1173330043385774402 *t+1) Then for all i>=0 we have 3 3 3 11 a(i) + 26 b(i) + 26 c(i) = -1375 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 279, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 3 (32092701928400098939 t + 52418163290347822474 t - 5) ) a(i) t = -------------------------------------------------------- / 2 ----- (t - 1) (t - 34813534449313428482 t + 1) i = 0 infinity ----- 2 \ i 2 (36707519254366654849 t + 32642426981977110142 t + 1) ) b(i) t = - -------------------------------------------------------- / 2 ----- (t - 1) (t - 34813534449313428482 t + 1) i = 0 infinity ----- 2 \ i 13 (2737807457712443425 t - 13407029955611484194 t + 1) ) c(i) t = -------------------------------------------------------- / 2 ----- (t - 1) (t - 34813534449313428482 t + 1) i = 0 In Maple notation, these generating functions are 3*(32092701928400098939*t^2+52418163290347822474*t-5)/(t-1)/(t^2-\ 34813534449313428482*t+1) -2*(36707519254366654849*t^2+32642426981977110142*t+1)/(t-1)/(t^2-\ 34813534449313428482*t+1) 13*(2737807457712443425*t^2-13407029955611484194*t+1)/(t-1)/(t^2-\ 34813534449313428482*t+1) Then for all i>=0 we have 3 3 3 11 a(i) + 28 b(i) + 28 c(i) = -24167 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 280, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (107051683967557766845819176391302167097001 t / ----- i = 0 / + 1040130922003888648191144034163692432126318 t - 23) / ((t - 1) / 2 (t - 343900276498927779993055249753175030992898 t + 1)) infinity ----- \ i 2 ) b(i) t = - 6 (13497914407973662919830694332573792089601 t / ----- i = 0 / + 87986070978851463646112529230111531579902 t + 1) / ((t - 1) / 2 (t - 343900276498927779993055249753175030992898 t + 1)) infinity ----- \ i 2 ) c(i) t = (40381675287733859060225168053914344328401 t / ----- i = 0 / - 649285587608684618455884509430026286345442 t + 17) / ((t - 1) / 2 (t - 343900276498927779993055249753175030992898 t + 1)) In Maple notation, these generating functions are (107051683967557766845819176391302167097001*t^2+ 1040130922003888648191144034163692432126318*t-23)/(t-1)/(t^2-\ 343900276498927779993055249753175030992898*t+1) -6*(13497914407973662919830694332573792089601*t^2+ 87986070978851463646112529230111531579902*t+1)/(t-1)/(t^2-\ 343900276498927779993055249753175030992898*t+1) (40381675287733859060225168053914344328401*t^2-\ 649285587608684618455884509430026286345442*t+17)/(t-1)/(t^2-\ 343900276498927779993055249753175030992898*t+1) Then for all i>=0 we have 3 3 3 11 a(i) + 29 b(i) + 29 c(i) = -2376 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 281, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 20 ( / ----- i = 0 2 1472314165290099863115106921591 t + 4977093357367800478827296574090 t - 1) / 2 / ((t - 1) (t - 21368881953326536708985509913602 t + 1)) / infinity ----- \ i ) b(i) t = - 4 ( / ----- i = 0 2 5488862000290802169259700211001 t + 10658333045423911609024878291398 t + 1 / 2 ) / ((t - 1) (t - 21368881953326536708985509913602 t + 1)) / infinity ----- \ i ) c(i) t = 5 ( / ----- i = 0 2 2301353365627338703889543892995 t - 15219109402199109726517206694918 t + 3 / 2 ) / ((t - 1) (t - 21368881953326536708985509913602 t + 1)) / In Maple notation, these generating functions are 20*(1472314165290099863115106921591*t^2+4977093357367800478827296574090*t-1)/(t -1)/(t^2-21368881953326536708985509913602*t+1) -4*(5488862000290802169259700211001*t^2+10658333045423911609024878291398*t+1)/( t-1)/(t^2-21368881953326536708985509913602*t+1) 5*(2301353365627338703889543892995*t^2-15219109402199109726517206694918*t+3)/(t -1)/(t^2-21368881953326536708985509913602*t+1) Then for all i>=0 we have 3 3 3 11 a(i) + 31 b(i) + 31 c(i) = -14641 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 282, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 25 (279948031 t + 2402300994 t - 1) ) a(i) t = ------------------------------------ / 2 ----- (t - 1) (t - 17555720002 t + 1) i = 0 infinity ----- 2 \ i 7 (740496121 t + 3923363078 t + 1) ) b(i) t = - ----------------------------------- / 2 ----- (t - 1) (t - 17555720002 t + 1) i = 0 infinity ----- 2 \ i 2 (1388834729 t - 17712341938 t + 9) ) c(i) t = ------------------------------------- / 2 ----- (t - 1) (t - 17555720002 t + 1) i = 0 In Maple notation, these generating functions are 25*(279948031*t^2+2402300994*t-1)/(t-1)/(t^2-17555720002*t+1) -7*(740496121*t^2+3923363078*t+1)/(t-1)/(t^2-17555720002*t+1) 2*(1388834729*t^2-17712341938*t+9)/(t-1)/(t^2-17555720002*t+1) Then for all i>=0 we have 3 3 3 11 a(i) + 32 b(i) + 32 c(i) = -3773 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 283, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = ( / ----- i = 0 2 2117184861786154984794379401923409676823479867813928937101 t / + 3821509049269027451939580584037857709872276921654177078918 t - 19) / ( / (t - 1) 2 (t - 732756231853171297783614791527156789759994323139467910402 t + 1)) infinity ----- \ i ) b(i) t = - 4 ( / ----- i = 0 2 387185951360832668236505875584236772901148236327942487521 t / + 297484678335418327860442655472950034319632601915297848478 t + 1) / ( / (t - 1) 2 (t - 732756231853171297783614791527156789759994323139467910402 t + 1)) infinity ----- \ i ) c(i) t = 15 ( / ----- i = 0 2 57584815500834388328287501290781754253917414891464627441 t / - 240163650086501320620807109572698236179458971756328717042 t + 1) / ( / (t - 1) 2 (t - 732756231853171297783614791527156789759994323139467910402 t + 1)) In Maple notation, these generating functions are (2117184861786154984794379401923409676823479867813928937101*t^2+ 3821509049269027451939580584037857709872276921654177078918*t-19)/(t-1)/(t^2-\ 732756231853171297783614791527156789759994323139467910402*t+1) -4*(387185951360832668236505875584236772901148236327942487521*t^2+ 297484678335418327860442655472950034319632601915297848478*t+1)/(t-1)/(t^2-\ 732756231853171297783614791527156789759994323139467910402*t+1) 15*(57584815500834388328287501290781754253917414891464627441*t^2-\ 240163650086501320620807109572698236179458971756328717042*t+1)/(t-1)/(t^2-\ 732756231853171297783614791527156789759994323139467910402*t+1) Then for all i>=0 we have 3 3 3 11 a(i) + 34 b(i) + 34 c(i) = -37125 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 284, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 7642689293 t + 59439047438 t - 27 ) a(i) t = ---------------------------------- / 2 ----- (t - 1) (t - 15586523714 t + 1) i = 0 infinity ----- 2 \ i 8 (694835153 t + 3072152686 t + 1) ) b(i) t = - ----------------------------------- / 2 ----- (t - 1) (t - 15586523714 t + 1) i = 0 infinity ----- 2 \ i 3156693163 t - 33292595902 t + 19 ) c(i) t = ---------------------------------- / 2 ----- (t - 1) (t - 15586523714 t + 1) i = 0 In Maple notation, these generating functions are (7642689293*t^2+59439047438*t-27)/(t-1)/(t^2-15586523714*t+1) -8*(694835153*t^2+3072152686*t+1)/(t-1)/(t^2-15586523714*t+1) (3156693163*t^2-33292595902*t+19)/(t-1)/(t^2-15586523714*t+1) Then for all i>=0 we have 3 3 3 11 a(i) + 35 b(i) + 35 c(i) = -5632 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 285, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 338899 t + 636994 t - 21 ) a(i) t = --------------------------- / 2 ----- (t - 1) (t - 114242 t + 1) i = 0 infinity ----- 2 \ i 243869 t + 172894 t + 5 ) b(i) t = - --------------------------- / 2 ----- (t - 1) (t - 114242 t + 1) i = 0 infinity ----- 2 \ i 16 (8945 t - 34994 t + 1) ) c(i) t = --------------------------- / 2 ----- (t - 1) (t - 114242 t + 1) i = 0 In Maple notation, these generating functions are (338899*t^2+636994*t-21)/(t-1)/(t^2-114242*t+1) -(243869*t^2+172894*t+5)/(t-1)/(t^2-114242*t+1) 16*(8945*t^2-34994*t+1)/(t-1)/(t^2-114242*t+1) Then for all i>=0 we have 3 3 3 11 a(i) + 37 b(i) + 37 c(i) = -45056 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 286, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 635635 t + 4563946 t - 29 ) a(i) t = ---------------------------- / 2 ----- (t - 1) (t - 1085762 t + 1) i = 0 infinity ----- 2 \ i 9 (50569 t + 190198 t + 1) ) b(i) t = - ---------------------------- / 2 ----- (t - 1) (t - 1085762 t + 1) i = 0 infinity ----- 2 \ i 4 (67781 t - 609514 t + 5) ) c(i) t = ---------------------------- / 2 ----- (t - 1) (t - 1085762 t + 1) i = 0 In Maple notation, these generating functions are (635635*t^2+4563946*t-29)/(t-1)/(t^2-1085762*t+1) -9*(50569*t^2+190198*t+1)/(t-1)/(t^2-1085762*t+1) 4*(67781*t^2-609514*t+5)/(t-1)/(t^2-1085762*t+1) Then for all i>=0 we have 3 3 3 11 a(i) + 38 b(i) + 38 c(i) = -8019 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 287, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 408617 t + 795822 t - 23 ) a(i) t = --------------------------- / 2 ----- (t - 1) (t - 133954 t + 1) i = 0 infinity ----- 2 \ i 2 (144931 t + 94426 t + 3) ) b(i) t = - --------------------------- / 2 ----- (t - 1) (t - 133954 t + 1) i = 0 infinity ----- 2 \ i 17 (10441 t - 38602 t + 1) ) c(i) t = --------------------------- / 2 ----- (t - 1) (t - 133954 t + 1) i = 0 In Maple notation, these generating functions are (408617*t^2+795822*t-23)/(t-1)/(t^2-133954*t+1) -2*(144931*t^2+94426*t+3)/(t-1)/(t^2-133954*t+1) 17*(10441*t^2-38602*t+1)/(t-1)/(t^2-133954*t+1) Then for all i>=0 we have 3 3 3 11 a(i) + 40 b(i) + 40 c(i) = -54043 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 288, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 2 (4323968601008859135344847798914005384949 t / ----- i = 0 / + 6346595661870196851608003521283668394262 t - 11) / ((t - 1) / 2 (t - 2129372314483594199853413641212664217602 t + 1)) infinity ----- \ i 2 ) b(i) t = - 2 (3053924972513043053761625573586358201603 t / ----- i = 0 / + 1091143487916288772350119426766054265594 t + 3) / ((t - 1) / 2 (t - 2129372314483594199853413641212664217602 t + 1)) infinity ----- \ i 2 ) c(i) t = (3787671671314015351972357206292030586897 t / ----- i = 0 / - 12077808592172679004195847206996855521314 t + 17) / ((t - 1) / 2 (t - 2129372314483594199853413641212664217602 t + 1)) In Maple notation, these generating functions are 2*(4323968601008859135344847798914005384949*t^2+ 6346595661870196851608003521283668394262*t-11)/(t-1)/(t^2-\ 2129372314483594199853413641212664217602*t+1) -2*(3053924972513043053761625573586358201603*t^2+ 1091143487916288772350119426766054265594*t+3)/(t-1)/(t^2-\ 2129372314483594199853413641212664217602*t+1) (3787671671314015351972357206292030586897*t^2-\ 12077808592172679004195847206996855521314*t+17)/(t-1)/(t^2-\ 2129372314483594199853413641212664217602*t+1) Then for all i>=0 we have 3 3 3 11 a(i) + 41 b(i) + 41 c(i) = -75449 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 289, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (12336700289448732350511224321660633730008724917687 t / ----- i = 0 / + 24793447224906081698398806076607267904932358411362 t - 25) / ((t - 1) / 2 (t - 3929501951746112597914236873343792505225282668802 t + 1)) infinity ----- \ i 2 ) b(i) t = - (8642043461101431518733501185826353400878598718423 t / ----- i = 0 / + 5154154319173373701324978294441295831899981340194 t + 7) / ((t - 1) / 2 (t - 3929501951746112597914236873343792505225282668802 t + 1)) infinity ----- \ i 2 ) c(i) t = 18 (304785743725355942441753337793625613963415724545 t / ----- i = 0 / - 1071241175962845121333891086697383904673336838914 t + 1) / ((t - 1) / 2 (t - 3929501951746112597914236873343792505225282668802 t + 1)) In Maple notation, these generating functions are (12336700289448732350511224321660633730008724917687*t^2+ 24793447224906081698398806076607267904932358411362*t-25)/(t-1)/(t^2-\ 3929501951746112597914236873343792505225282668802*t+1) -(8642043461101431518733501185826353400878598718423*t^2+ 5154154319173373701324978294441295831899981340194*t+7)/(t-1)/(t^2-\ 3929501951746112597914236873343792505225282668802*t+1) 18*(304785743725355942441753337793625613963415724545*t^2-\ 1071241175962845121333891086697383904673336838914*t+1)/(t-1)/(t^2-\ 3929501951746112597914236873343792505225282668802*t+1) Then for all i>=0 we have 3 3 3 11 a(i) + 43 b(i) + 43 c(i) = -64152 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 290, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 53297146009526415929269 t + 110153614485880903236262 t - 27 ) a(i) t = ------------------------------------------------------------ / 2 ----- (t - 1) (t - 16487959843945291980098 t + 1) i = 0 infinity ----- \ i ) b(i) t = / ----- i = 0 2 8 (4615358143747890476393 t + 2509563014994020576134 t + 1) - ------------------------------------------------------------ 2 (t - 1) (t - 16487959843945291980098 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 19 (1272520813265941785001 t - 4272487616946746438698 t + 1) ------------------------------------------------------------- 2 (t - 1) (t - 16487959843945291980098 t + 1) In Maple notation, these generating functions are (53297146009526415929269*t^2+110153614485880903236262*t-27)/(t-1)/(t^2-\ 16487959843945291980098*t+1) -8*(4615358143747890476393*t^2+2509563014994020576134*t+1)/(t-1)/(t^2-\ 16487959843945291980098*t+1) 19*(1272520813265941785001*t^2-4272487616946746438698*t+1)/(t-1)/(t^2-\ 16487959843945291980098*t+1) Then for all i>=0 we have 3 3 3 11 a(i) + 46 b(i) + 46 c(i) = -75449 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 291, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 1486927040952945573490316051 t + 3151161804549556940214771978 t - 29 --------------------------------------------------------------------- 2 (t - 1) (t - 446709288258178258556422402 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 1019952614759797117683474329 t + 503465963988434969389677662 t + 9 - ------------------------------------------------------------------- 2 (t - 1) (t - 446709288258178258556422402 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 20 (34307633339538425977649761 t - 110478562276950030331307362 t + 1) ---------------------------------------------------------------------- 2 (t - 1) (t - 446709288258178258556422402 t + 1) In Maple notation, these generating functions are (1486927040952945573490316051*t^2+3151161804549556940214771978*t-29)/(t-1)/(t^2 -446709288258178258556422402*t+1) -(1019952614759797117683474329*t^2+503465963988434969389677662*t+9)/(t-1)/(t^2-\ 446709288258178258556422402*t+1) 20*(34307633339538425977649761*t^2-110478562276950030331307362*t+1)/(t-1)/(t^2-\ 446709288258178258556422402*t+1) Then for all i>=0 we have 3 3 3 11 a(i) + 49 b(i) + 49 c(i) = -88000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 292, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 2 (162246154538805775048462746282099400556653953663951870\ / ----- i = 0 2 52349401444259842835269 t + 3141414769537951592030674201183792711380128\ / 2 2161255759578849627952190275526342 t - 11) / ((t - 1) (t - 1019399579\ / 2578145303464919520523465481697837760211571871613050555858810700802 t + 1)) infinity ----- \ i ) b(i) t = - (190777416303384883730022526646762651821817888978212101\ / ----- i = 0 2 99385942242665219706883 t + 1879828404268504017957859754582297998199465\ / 2 4265869620132383533406918116254714 t + 3) / ((t - 1) (t - 10193995792\ / 578145303464919520523465481697837760211571871613050555858810700802 t + 1)) infinity ----- \ i ) c(i) t = 2 (496269722561318386462140784745840590872373165326068054\ / ----- i = 0 2 6466216867823423412727 t - 23900710062124948140911832952708028490811953\ / 2 235106095712350954692615091393534 t + 7) / ((t - 1) (t - 101939957925\ / 78145303464919520523465481697837760211571871613050555858810700802 t + 1)) In Maple notation, these generating functions are 2*( 16224615453880577504846274628209940055665395366395187052349401444259842835269*t ^2+ 31414147695379515920306742011837927113801282161255759578849627952190275526342*t -11)/(t-1)/(t^2-\ 10193995792578145303464919520523465481697837760211571871613050555858810700802*t +1) -(19077741630338488373002252664676265182181788897821210199385942242665219706883 *t^2+ 18798284042685040179578597545822979981994654265869620132383533406918116254714*t +3)/(t-1)/(t^2-\ 10193995792578145303464919520523465481697837760211571871613050555858810700802*t +1) 2*(4962697225613183864621407847458405908723731653260680546466216867823423412727 *t^2-\ 23900710062124948140911832952708028490811953235106095712350954692615091393534*t +7)/(t-1)/(t^2-\ 10193995792578145303464919520523465481697837760211571871613050555858810700802*t +1) Then for all i>=0 we have 3 3 3 11 a(i) + 63 b(i) + 63 c(i) = -54043 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 293, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 2 / ----- i = 0 2 (8039700328214619714619662323 t + 22500518829820478919476551706 t - 13) / 2 / ((t - 1) (t - 6999092217551068095641026562 t + 1)) / infinity ----- \ i ) b(i) t = / ----- i = 0 2 4 (2272747109378145261073522689 t + 3393101258972331390066171902 t + 1) - ------------------------------------------------------------------------ 2 (t - 1) (t - 6999092217551068095641026562 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 4879716837019208812826648591 t - 27543110310421115417385426974 t + 15 ---------------------------------------------------------------------- 2 (t - 1) (t - 6999092217551068095641026562 t + 1) In Maple notation, these generating functions are 2*(8039700328214619714619662323*t^2+22500518829820478919476551706*t-13)/(t-1)/( t^2-6999092217551068095641026562*t+1) -4*(2272747109378145261073522689*t^2+3393101258972331390066171902*t+1)/(t-1)/(t ^2-6999092217551068095641026562*t+1) (4879716837019208812826648591*t^2-27543110310421115417385426974*t+15)/(t-1)/(t^ 2-6999092217551068095641026562*t+1) Then for all i>=0 we have 3 3 3 11 a(i) + 72 b(i) + 72 c(i) = -45056 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 294, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 9 (1139753314520983957 t + 3400764650218830446 t - 3) ) a(i) t = ------------------------------------------------------ / 2 ----- (t - 1) (t - 4673598872813236802 t + 1) i = 0 infinity ----- 2 \ i 4 (1403797967844937561 t + 2294064474377072038 t + 1) ) b(i) t = - ------------------------------------------------------ / 2 ----- (t - 1) (t - 4673598872813236802 t + 1) i = 0 infinity ----- 2 \ i 15 (199407243925196665 t - 1185503895184399226 t + 1) ) c(i) t = ------------------------------------------------------ / 2 ----- (t - 1) (t - 4673598872813236802 t + 1) i = 0 In Maple notation, these generating functions are 9*(1139753314520983957*t^2+3400764650218830446*t-3)/(t-1)/(t^2-\ 4673598872813236802*t+1) -4*(1403797967844937561*t^2+2294064474377072038*t+1)/(t-1)/(t^2-\ 4673598872813236802*t+1) 15*(199407243925196665*t^2-1185503895184399226*t+1)/(t-1)/(t^2-\ 4673598872813236802*t+1) Then for all i>=0 we have 3 3 3 11 a(i) + 79 b(i) + 79 c(i) = -45056 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 295, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = ( / ----- i = 0 2 4121320105067939183907784529251 t + 5958257263449180357053216430778 t - 29 / 2 ) / ((t - 1) (t - 771911262344609394531166310402 t + 1)) / infinity ----- \ i ) b(i) t = - 12 / ----- i = 0 2 (328173535913489425038603919681 t + 79845338074459941686953840318 t + 1) / 2 / ((t - 1) (t - 771911262344609394531166310402 t + 1)) / infinity ----- \ i ) c(i) t = 30 / ----- i = 0 2 (85476968753529779083132850881 t - 248684518348709525773355954882 t + 1) / 2 / ((t - 1) (t - 771911262344609394531166310402 t + 1)) / In Maple notation, these generating functions are (4121320105067939183907784529251*t^2+5958257263449180357053216430778*t-29)/(t-1 )/(t^2-771911262344609394531166310402*t+1) -12*(328173535913489425038603919681*t^2+79845338074459941686953840318*t+1)/(t-1 )/(t^2-771911262344609394531166310402*t+1) 30*(85476968753529779083132850881*t^2-248684518348709525773355954882*t+1)/(t-1) /(t^2-771911262344609394531166310402*t+1) Then for all i>=0 we have 3 3 3 12 a(i) + 19 b(i) + 19 c(i) = -187500 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 296, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 3390935181813981341 t + 9475476458533142966 t - 19 ) a(i) t = --------------------------------------------------- / 2 ----- (t - 1) (t - 2264931131112566594 t + 1) i = 0 infinity ----- 2 \ i 6 (368304948729392217 t + 261372619313697062 t + 1) ) b(i) t = - ---------------------------------------------------- / 2 ----- (t - 1) (t - 2264931131112566594 t + 1) i = 0 infinity ----- 2 \ i 12 (127636888001129753 t - 442475672022674394 t + 1) ) c(i) t = ----------------------------------------------------- / 2 ----- (t - 1) (t - 2264931131112566594 t + 1) i = 0 In Maple notation, these generating functions are (3390935181813981341*t^2+9475476458533142966*t-19)/(t-1)/(t^2-\ 2264931131112566594*t+1) -6*(368304948729392217*t^2+261372619313697062*t+1)/(t-1)/(t^2-\ 2264931131112566594*t+1) 12*(127636888001129753*t^2-442475672022674394*t+1)/(t-1)/(t^2-\ 2264931131112566594*t+1) Then for all i>=0 we have 3 3 3 12 a(i) + 65 b(i) + 65 c(i) = -15972 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 297, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (71230671356221696887728111395051 t / ----- i = 0 / + 537805712656590161619266217748978 t - 29) / ((t - 1) / 2 (t - 103633544562037968108294949790402 t + 1)) infinity ----- \ i 2 ) b(i) t = - 3 (12375747835756953436261533314481 t / ----- i = 0 / + 72002294709534920388863791149518 t + 1) / ((t - 1) / 2 (t - 103633544562037968108294949790402 t + 1)) infinity ----- \ i ) c(i) t = 15 ( / ----- i = 0 2 1014007590613509725452755659921 t - 17889616099671884490477820552722 t + 1 / 2 ) / ((t - 1) (t - 103633544562037968108294949790402 t + 1)) / In Maple notation, these generating functions are (71230671356221696887728111395051*t^2+537805712656590161619266217748978*t-29)/( t-1)/(t^2-103633544562037968108294949790402*t+1) -3*(12375747835756953436261533314481*t^2+72002294709534920388863791149518*t+1)/ (t-1)/(t^2-103633544562037968108294949790402*t+1) 15*(1014007590613509725452755659921*t^2-17889616099671884490477820552722*t+1)/( t-1)/(t^2-103633544562037968108294949790402*t+1) Then for all i>=0 we have 3 3 3 12 a(i) + 91 b(i) + 91 c(i) = -12000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 298, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 9 (2890319 t + 6136754 t - 1) ) a(i) t = ------------------------------ / 2 ----- (t - 1) (t - 26894594 t + 1) i = 0 infinity ----- 2 \ i 8 (4228597 t - 1195958 t + 1) ) b(i) t = - ------------------------------ / 2 ----- (t - 1) (t - 26894594 t + 1) i = 0 infinity ----- 2 \ i 28626203 t - 52887334 t + 11 ) c(i) t = ----------------------------- / 2 ----- (t - 1) (t - 26894594 t + 1) i = 0 In Maple notation, these generating functions are 9*(2890319*t^2+6136754*t-1)/(t-1)/(t^2-26894594*t+1) -8*(4228597*t^2-1195958*t+1)/(t-1)/(t^2-26894594*t+1) (28626203*t^2-52887334*t+11)/(t-1)/(t^2-26894594*t+1) Then for all i>=0 we have 3 3 3 13 a(i) + 15 b(i) + 15 c(i) = -2808 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 299, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 26 (10385560298159999 t + 14709592985040002 t - 1) ) a(i) t = --------------------------------------------------- / 2 ----- (t - 1) (t - 58468448039040002 t + 1) i = 0 infinity ----- 2 \ i 314127135727048819 t - 71779655449288838 t + 19 ) b(i) t = - ------------------------------------------------ / 2 ----- (t - 1) (t - 58468448039040002 t + 1) i = 0 infinity ----- 2 \ i 246620993789008831 t - 488968474066768862 t + 31 ) c(i) t = ------------------------------------------------- / 2 ----- (t - 1) (t - 58468448039040002 t + 1) i = 0 In Maple notation, these generating functions are 26*(10385560298159999*t^2+14709592985040002*t-1)/(t-1)/(t^2-58468448039040002*t +1) -(314127135727048819*t^2-71779655449288838*t+19)/(t-1)/(t^2-58468448039040002*t +1) (246620993789008831*t^2-488968474066768862*t+31)/(t-1)/(t^2-58468448039040002*t +1) Then for all i>=0 we have 3 3 3 13 a(i) + 16 b(i) + 16 c(i) = -138424 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 300, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 5 (162455362051889741853935947 t + 332384765731393610658730618 t - 5) ---------------------------------------------------------------------- 2 (t - 1) (t - 289687464394836993624686402 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 1043142410525734477862001023 t - 426568449390014006680084246 t + 23 - -------------------------------------------------------------------- 2 (t - 1) (t - 289687464394836993624686402 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 30 (30258764738305323099457369 t - 50811230109496005472187930 t + 1) --------------------------------------------------------------------- 2 (t - 1) (t - 289687464394836993624686402 t + 1) In Maple notation, these generating functions are 5*(162455362051889741853935947*t^2+332384765731393610658730618*t-5)/(t-1)/(t^2-\ 289687464394836993624686402*t+1) -(1043142410525734477862001023*t^2-426568449390014006680084246*t+23)/(t-1)/(t^2 -289687464394836993624686402*t+1) 30*(30258764738305323099457369*t^2-50811230109496005472187930*t+1)/(t-1)/(t^2-\ 289687464394836993624686402*t+1) Then for all i>=0 we have 3 3 3 13 a(i) + 18 b(i) + 18 c(i) = -63869 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 301, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 2 ( / ----- i = 0 2 37911718170125224221846252592434907007516716824024045434890668501049 t + 84129039521459703495939778345030917914218890292614422275648573637362 t / 2 - 11) / ((t - 1) (t / - 24304527844729636762240571596958914245784931637100283882623328347202 t + 1)) infinity ----- \ i ) b(i) t = - ( / ----- i = 0 2 68332803875868965707428015271175149611694737514580024415475613166721 t + 108621404632016255937019386773541479009563161118030449814513827727678 t / 2 + 1) / ((t - 1) (t / - 24304527844729636762240571596958914245784931637100283882623328347202 t + 1)) infinity ----- \ i ) c(i) t = 2 ( / ----- i = 0 2 13752399846328592888104487008891855647953752005892449281258215852031 t - 102229504100271203710328188031250169958582701322197686396252936299242 t / 2 + 11) / ((t - 1) (t / - 24304527844729636762240571596958914245784931637100283882623328347202 t + 1)) In Maple notation, these generating functions are 2*(37911718170125224221846252592434907007516716824024045434890668501049*t^2+ 84129039521459703495939778345030917914218890292614422275648573637362*t-11)/(t-1 )/(t^2-24304527844729636762240571596958914245784931637100283882623328347202*t+1 ) -(68332803875868965707428015271175149611694737514580024415475613166721*t^2+ 108621404632016255937019386773541479009563161118030449814513827727678*t+1)/(t-1 )/(t^2-24304527844729636762240571596958914245784931637100283882623328347202*t+1 ) 2*(13752399846328592888104487008891855647953752005892449281258215852031*t^2-\ 102229504100271203710328188031250169958582701322197686396252936299242*t+11)/(t-\ 1)/(t^2-24304527844729636762240571596958914245784931637100283882623328347202*t+ 1) Then for all i>=0 we have 3 3 3 13 a(i) + 19 b(i) + 19 c(i) = -63869 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 302, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (527737159136941975126076076255313655981 t / ----- i = 0 / + 12721526454707713876346046928587454344038 t - 19) / ((t - 1) / 2 (t - 6863514748069043356655303825727696000002 t + 1)) infinity ----- \ i 2 ) b(i) t = - 3 (149003077426302026971337345757912780001 t / ----- i = 0 / + 3183705272230313253170287262320391219998 t + 1) / ((t - 1) / 2 (t - 6863514748069043356655303825727696000002 t + 1)) infinity ----- \ i 2 ) c(i) t = 16 (8447784208396841203037715422452176001 t / ----- i = 0 / - 633330599769012206229592329437134176002 t + 1) / ((t - 1) / 2 (t - 6863514748069043356655303825727696000002 t + 1)) In Maple notation, these generating functions are (527737159136941975126076076255313655981*t^2+ 12721526454707713876346046928587454344038*t-19)/(t-1)/(t^2-\ 6863514748069043356655303825727696000002*t+1) -3*(149003077426302026971337345757912780001*t^2+ 3183705272230313253170287262320391219998*t+1)/(t-1)/(t^2-\ 6863514748069043356655303825727696000002*t+1) 16*(8447784208396841203037715422452176001*t^2-\ 633330599769012206229592329437134176002*t+1)/(t-1)/(t^2-\ 6863514748069043356655303825727696000002*t+1) Then for all i>=0 we have 3 3 3 13 a(i) + 22 b(i) + 22 c(i) = -351 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 303, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 26779 t + 457594 t - 21 ) a(i) t = --------------------------- / 2 ----- (t - 1) (t - 198914 t + 1) i = 0 infinity ----- 2 \ i 4 (5473 t + 77726 t + 1) ) b(i) t = - --------------------------- / 2 ----- (t - 1) (t - 198914 t + 1) i = 0 infinity ----- 2 \ i 7969 t - 340786 t + 17 ) c(i) t = --------------------------- / 2 ----- (t - 1) (t - 198914 t + 1) i = 0 In Maple notation, these generating functions are (26779*t^2+457594*t-21)/(t-1)/(t^2-198914*t+1) -4*(5473*t^2+77726*t+1)/(t-1)/(t^2-198914*t+1) (7969*t^2-340786*t+17)/(t-1)/(t^2-198914*t+1) Then for all i>=0 we have 3 3 3 13 a(i) + 25 b(i) + 25 c(i) = -832 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 304, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = ( / ----- i = 0 2 1473273018706890759560924280686333403576517433229053459766138919 t + 2582158746709182675722394779588784848344529167321793162445218034 t - 25) / / ((t - 1) ( / 2 t - 416291054680634637813703897564635132242735280011751706274028802 t + 1) ) infinity ----- \ i ) b(i) t = - 4 ( / ----- i = 0 2 334609386121613864322952450492308904730499058510230559410621467 t + 39295670264265246731537959320290650411157720263960973133688034 t + 3) / / ((t - 1) ( / 2 t - 416291054680634637813703897564635132242735280011751706274028802 t + 1) ) infinity ----- \ i ) c(i) t = 23 ( / ----- i = 0 2 42179099556944902930503423121637055131646385901463429247867441 t - 107206065884923878766066972654263064721499738731757608820790834 t + 1) / / ((t - 1) ( / 2 t - 416291054680634637813703897564635132242735280011751706274028802 t + 1) ) In Maple notation, these generating functions are (1473273018706890759560924280686333403576517433229053459766138919*t^2+ 2582158746709182675722394779588784848344529167321793162445218034*t-25)/(t-1)/(t ^2-416291054680634637813703897564635132242735280011751706274028802*t+1) -4*(334609386121613864322952450492308904730499058510230559410621467*t^2+ 39295670264265246731537959320290650411157720263960973133688034*t+3)/(t-1)/(t^2-\ 416291054680634637813703897564635132242735280011751706274028802*t+1) 23*(42179099556944902930503423121637055131646385901463429247867441*t^2-\ 107206065884923878766066972654263064721499738731757608820790834*t+1)/(t-1)/(t^2 -416291054680634637813703897564635132242735280011751706274028802*t+1) Then for all i>=0 we have 3 3 3 13 a(i) + 28 b(i) + 28 c(i) = -89167 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 305, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = ( / ----- i = 0 2 144553823073260762618856252643 t + 4225644870058067110868940307834 t - 29) / 2 / ((t - 1) (t - 2580329314077089845013768920898 t + 1)) / infinity ----- \ i ) b(i) t = - 9 / ----- i = 0 2 (12342312849422391072987993673 t + 261000441073691786550064685494 t + 1) / 2 / ((t - 1) (t - 2580329314077089845013768920898 t + 1)) / infinity ----- \ i ) c(i) t = 2 / ----- i = 0 2 (26177912510644667421490795211 t - 1256220305164658466725227851478 t + 11) / 2 / ((t - 1) (t - 2580329314077089845013768920898 t + 1)) / In Maple notation, these generating functions are (144553823073260762618856252643*t^2+4225644870058067110868940307834*t-29)/(t-1) /(t^2-2580329314077089845013768920898*t+1) -9*(12342312849422391072987993673*t^2+261000441073691786550064685494*t+1)/(t-1) /(t^2-2580329314077089845013768920898*t+1) 2*(26177912510644667421490795211*t^2-1256220305164658466725227851478*t+11)/(t-1 )/(t^2-2580329314077089845013768920898*t+1) Then for all i>=0 we have 3 3 3 13 a(i) + 32 b(i) + 32 c(i) = -351 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 306, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 1677397 t + 16476934 t - 27 ) a(i) t = ---------------------------- / 2 ----- (t - 1) (t - 4656962 t + 1) i = 0 infinity ----- 2 \ i 7 (181609 t + 1204502 t + 1) ) b(i) t = - ----------------------------- / 2 ----- (t - 1) (t - 4656962 t + 1) i = 0 infinity ----- 2 \ i 4 (157477 t - 2583178 t + 5) ) c(i) t = ----------------------------- / 2 ----- (t - 1) (t - 4656962 t + 1) i = 0 In Maple notation, these generating functions are (1677397*t^2+16476934*t-27)/(t-1)/(t^2-4656962*t+1) -7*(181609*t^2+1204502*t+1)/(t-1)/(t^2-4656962*t+1) 4*(157477*t^2-2583178*t+5)/(t-1)/(t^2-4656962*t+1) Then for all i>=0 we have 3 3 3 13 a(i) + 34 b(i) + 34 c(i) = -4459 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 307, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 4 (116162380793 t + 4647657139214 t - 7) ) a(i) t = ----------------------------------------- / 2 ----- (t - 1) (t - 17660989440002 t + 1) i = 0 infinity ----- 2 \ i 353058216011 t + 8709817943978 t + 11 ) b(i) t = - -------------------------------------- / 2 ----- (t - 1) (t - 17660989440002 t + 1) i = 0 infinity ----- 2 \ i 3 (66058347207 t - 3087017067214 t + 7) ) c(i) t = ---------------------------------------- / 2 ----- (t - 1) (t - 17660989440002 t + 1) i = 0 In Maple notation, these generating functions are 4*(116162380793*t^2+4647657139214*t-7)/(t-1)/(t^2-17660989440002*t+1) -(353058216011*t^2+8709817943978*t+11)/(t-1)/(t^2-17660989440002*t+1) 3*(66058347207*t^2-3087017067214*t+7)/(t-1)/(t^2-17660989440002*t+1) Then for all i>=0 we have 3 3 3 13 a(i) + 36 b(i) + 36 c(i) = -104 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 308, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (1707117286667401149669021126049811 t / ----- i = 0 / + 15035511161647270924664906396715018 t - 29) / ((t - 1) / 2 (t - 3820653989301942066498544606265602 t + 1)) infinity ----- \ i 2 ) b(i) t = - 8 (158771947613696118344040900516001 t / ----- i = 0 / + 880083094135446976051549803618398 t + 1) / ((t - 1) / 2 (t - 3820653989301942066498544606265602 t + 1)) infinity ----- \ i 2 ) c(i) t = (670377615323725299571319781461861 t / ----- i = 0 / - 8981217949316870054736045414537082 t + 21) / ((t - 1) / 2 (t - 3820653989301942066498544606265602 t + 1)) In Maple notation, these generating functions are (1707117286667401149669021126049811*t^2+15035511161647270924664906396715018*t-\ 29)/(t-1)/(t^2-3820653989301942066498544606265602*t+1) -8*(158771947613696118344040900516001*t^2+880083094135446976051549803618398*t+1 )/(t-1)/(t^2-3820653989301942066498544606265602*t+1) (670377615323725299571319781461861*t^2-8981217949316870054736045414537082*t+21) /(t-1)/(t^2-3820653989301942066498544606265602*t+1) Then for all i>=0 we have 3 3 3 13 a(i) + 37 b(i) + 37 c(i) = -6656 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 309, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 27 (221331466317419810548552035167680106319 t / ----- i = 0 / + 3027642500705391421177709803941371143282 t - 1) / ((t - 1) / 2 (t - 19256113999671783641694673826914620820802 t + 1)) infinity ----- \ i 2 ) b(i) t = - 2 (2107217634002535971896743437861190890041 t / ----- i = 0 / + 25707169254412262621662229867682150295558 t + 1) / ((t - 1) / 2 (t - 19256113999671783641694673826914620820802 t + 1)) infinity ----- \ i 2 ) c(i) t = (1226460472719904501388034400958700344779 t / ----- i = 0 / - 56855234249549501688505981012045382715998 t + 19) / ((t - 1) / 2 (t - 19256113999671783641694673826914620820802 t + 1)) In Maple notation, these generating functions are 27*(221331466317419810548552035167680106319*t^2+ 3027642500705391421177709803941371143282*t-1)/(t-1)/(t^2-\ 19256113999671783641694673826914620820802*t+1) -2*(2107217634002535971896743437861190890041*t^2+ 25707169254412262621662229867682150295558*t+1)/(t-1)/(t^2-\ 19256113999671783641694673826914620820802*t+1) (1226460472719904501388034400958700344779*t^2-\ 56855234249549501688505981012045382715998*t+19)/(t-1)/(t^2-\ 19256113999671783641694673826914620820802*t+1) Then for all i>=0 we have 3 3 3 13 a(i) + 38 b(i) + 38 c(i) = -4459 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 310, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 12 (189592718433717509374037684973599161233762239 t / ----- i = 0 / + 518527903176048060145953412323434325257381954 t - 1) / ((t - 1) / 2 (t - 1838733378801828243543506294662044935510618114 t + 1)) infinity ----- \ i 2 ) b(i) t = - (1609516088789837891837229687119912046747218305 t / ----- i = 0 / + 3031946809156524664680359017852240217648516734 t + 1) / ((t - 1) / 2 (t - 1838733378801828243543506294662044935510618114 t + 1)) infinity ----- \ i 2 ) c(i) t = 9 (77719004478665982982427644360737341425017729 t / ----- i = 0 / - 593437104250484044817715278246532037468988290 t + 1) / ((t - 1) / 2 (t - 1838733378801828243543506294662044935510618114 t + 1)) In Maple notation, these generating functions are 12*(189592718433717509374037684973599161233762239*t^2+ 518527903176048060145953412323434325257381954*t-1)/(t-1)/(t^2-\ 1838733378801828243543506294662044935510618114*t+1) -(1609516088789837891837229687119912046747218305*t^2+ 3031946809156524664680359017852240217648516734*t+1)/(t-1)/(t^2-\ 1838733378801828243543506294662044935510618114*t+1) 9*(77719004478665982982427644360737341425017729*t^2-\ 593437104250484044817715278246532037468988290*t+1)/(t-1)/(t^2-\ 1838733378801828243543506294662044935510618114*t+1) Then for all i>=0 we have 3 3 3 13 a(i) + 40 b(i) + 40 c(i) = -6656 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 311, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 4 ( / ----- i = 0 2 8400449299003827649082451863363 t + 35418968400660880714160324550548 t - 7 / 2 ) / ((t - 1) (t - 25029848421349555656149393232962 t + 1)) / infinity ----- \ i 2 ) b(i) t = - (24481770970779654188366871848455 t / ----- i = 0 / + 54892059560813513382094979735602 t + 7) / ((t - 1) / 2 (t - 25029848421349555656149393232962 t + 1)) infinity ----- \ i ) c(i) t = 4 ( / ----- i = 0 2 3456885647888821853480208834707 t - 23300343280787113746095671730728 t + 5 / 2 ) / ((t - 1) (t - 25029848421349555656149393232962 t + 1)) / In Maple notation, these generating functions are 4*(8400449299003827649082451863363*t^2+35418968400660880714160324550548*t-7)/(t -1)/(t^2-25029848421349555656149393232962*t+1) -(24481770970779654188366871848455*t^2+54892059560813513382094979735602*t+7)/(t -1)/(t^2-25029848421349555656149393232962*t+1) 4*(3456885647888821853480208834707*t^2-23300343280787113746095671730728*t+5)/(t -1)/(t^2-25029848421349555656149393232962*t+1) Then for all i>=0 we have 3 3 3 13 a(i) + 41 b(i) + 41 c(i) = -28561 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 312, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 4 (5474282854751066874861970367 t + 18400506740613327962558838200 t - 7) ------------------------------------------------------------------------- 2 (t - 1) (t - 11898498709124970708734776898 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 15807071888436122087376101383 t + 25608001451544317677149056050 t + 7 - ---------------------------------------------------------------------- 2 (t - 1) (t - 11898498709124970708734776898 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 20 (459350445064764851470174303 t - 2530104112063786839696432176 t + 1) ------------------------------------------------------------------------ 2 (t - 1) (t - 11898498709124970708734776898 t + 1) In Maple notation, these generating functions are 4*(5474282854751066874861970367*t^2+18400506740613327962558838200*t-7)/(t-1)/(t ^2-11898498709124970708734776898*t+1) -(15807071888436122087376101383*t^2+25608001451544317677149056050*t+7)/(t-1)/(t ^2-11898498709124970708734776898*t+1) 20*(459350445064764851470174303*t^2-2530104112063786839696432176*t+1)/(t-1)/(t^ 2-11898498709124970708734776898*t+1) Then for all i>=0 we have 3 3 3 13 a(i) + 43 b(i) + 43 c(i) = -43875 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 313, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 567751 t + 1070226 t - 25 ) a(i) t = --------------------------- / 2 ----- (t - 1) (t - 161602 t + 1) i = 0 infinity ----- 2 \ i 2 (204035 t + 143738 t + 3) ) b(i) t = - ---------------------------- / 2 ----- (t - 1) (t - 161602 t + 1) i = 0 infinity ----- 2 \ i 19 (12649 t - 49258 t + 1) ) c(i) t = --------------------------- / 2 ----- (t - 1) (t - 161602 t + 1) i = 0 In Maple notation, these generating functions are (567751*t^2+1070226*t-25)/(t-1)/(t^2-161602*t+1) -2*(204035*t^2+143738*t+3)/(t-1)/(t^2-161602*t+1) 19*(12649*t^2-49258*t+1)/(t-1)/(t^2-161602*t+1) Then for all i>=0 we have 3 3 3 13 a(i) + 44 b(i) + 44 c(i) = -89167 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 314, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 665117 t + 1292030 t - 27 ) a(i) t = --------------------------- / 2 ----- (t - 1) (t - 184898 t + 1) i = 0 infinity ----- 2 \ i 472303 t + 309770 t + 7 ) b(i) t = - --------------------------- / 2 ----- (t - 1) (t - 184898 t + 1) i = 0 infinity ----- 2 \ i 20 (14417 t - 53522 t + 1) ) c(i) t = --------------------------- / 2 ----- (t - 1) (t - 184898 t + 1) i = 0 In Maple notation, these generating functions are (665117*t^2+1292030*t-27)/(t-1)/(t^2-184898*t+1) -(472303*t^2+309770*t+7)/(t-1)/(t^2-184898*t+1) 20*(14417*t^2-53522*t+1)/(t-1)/(t^2-184898*t+1) Then for all i>=0 we have 3 3 3 13 a(i) + 47 b(i) + 47 c(i) = -104000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 315, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = (24144115242309261875055039579442459278591773946417373400\ / ----- i = 0 2 8021721019341719469971 t + 48188148168453791741499058553782986919953527\ / 2 7532661612814864593104840215210058 t - 29) / ((t - 1) (t - 6550944565\ / 0463070143837652926119942291306125437322207432733561379237326920002 t + 1)) infinity ----- \ i ) b(i) t = - 8 (2120006848453554046109318534424732190559656062391976\ / ----- i = 0 2 6056953750938203390155001 t + 12909022647933978438181454663440243408575\ / 2 266207765011615338479486979304094998 t + 1) / ((t - 1) (t - 655094456\ / 50463070143837652926119942291306125437322207432733561379237326920002 t + 1) ) infinity ----- \ i ) c(i) t = 21 (50869451545847734673143990403537229104968510824129979\ / ----- i = 0 2 81597350478123727341801 t - 1808088463362078066703807142423470017303849\ / 2 9399245294237708676354383801341802 t + 1) / ((t - 1) (t - 65509445650\ / 463070143837652926119942291306125437322207432733561379237326920002 t + 1)) In Maple notation, these generating functions are (241441152423092618750550395794424592785917739464173734008021721019341719469971 *t^2+ 481881481684537917414990585537829869199535277532661612814864593104840215210058* t-29)/(t-1)/(t^2-\ 65509445650463070143837652926119942291306125437322207432733561379237326920002*t +1) -8*( 21200068484535540461093185344247321905596560623919766056953750938203390155001*t ^2+ 12909022647933978438181454663440243408575266207765011615338479486979304094998*t +1)/(t-1)/(t^2-\ 65509445650463070143837652926119942291306125437322207432733561379237326920002*t +1) 21*( 5086945154584773467314399040353722910496851082412997981597350478123727341801*t^ 2-18080884633620780667038071424234700173038499399245294237708676354383801341802 *t+1)/(t-1)/(t^2-\ 65509445650463070143837652926119942291306125437322207432733561379237326920002*t +1) Then for all i>=0 we have 3 3 3 13 a(i) + 50 b(i) + 50 c(i) = -120393 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 316, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 238395750373896908599273 t + 654060152466085990453294 t - 23 ------------------------------------------------------------- 2 (t - 1) (t - 137227589737560697159682 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 293112628077182680197783 t - 218767778926397347916462 t + 23 - ------------------------------------------------------------- 2 (t - 1) (t - 137227589737560697159682 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 279868419723077296386713 t - 354213268873862628668082 t + 25 ------------------------------------------------------------- 2 (t - 1) (t - 137227589737560697159682 t + 1) In Maple notation, these generating functions are (238395750373896908599273*t^2+654060152466085990453294*t-23)/(t-1)/(t^2-\ 137227589737560697159682*t+1) -(293112628077182680197783*t^2-218767778926397347916462*t+23)/(t-1)/(t^2-\ 137227589737560697159682*t+1) (279868419723077296386713*t^2-354213268873862628668082*t+25)/(t-1)/(t^2-\ 137227589737560697159682*t+1) Then for all i>=0 we have 3 3 3 13 a(i) + 54 b(i) + 54 c(i) = -28561 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 317, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (79097233543191401729072324602456578274040051 t / ----- i = 0 / + 105903818449302558453020901149950801797706026 t - 29) / ((t - 1) / 2 (t - 13650769671864419452376428788031543852189954 t + 1)) infinity ----- \ i 2 ) b(i) t = - (54694629706983604499825416348069281534944569 t / ----- i = 0 / + 9114223247494534202633173334984879946627262 t + 9) / ((t - 1) / 2 (t - 13650769671864419452376428788031543852189954 t + 1)) infinity ----- \ i 2 ) c(i) t = 2 (17999459980205545681931433448289772425994827 t / ----- i = 0 / - 49903886457444615033160728289816853166780758 t + 11) / ((t - 1) / 2 (t - 13650769671864419452376428788031543852189954 t + 1)) In Maple notation, these generating functions are (79097233543191401729072324602456578274040051*t^2+ 105903818449302558453020901149950801797706026*t-29)/(t-1)/(t^2-\ 13650769671864419452376428788031543852189954*t+1) -(54694629706983604499825416348069281534944569*t^2+ 9114223247494534202633173334984879946627262*t+9)/(t-1)/(t^2-\ 13650769671864419452376428788031543852189954*t+1) 2*(17999459980205545681931433448289772425994827*t^2-\ 49903886457444615033160728289816853166780758*t+11)/(t-1)/(t^2-\ 13650769671864419452376428788031543852189954*t+1) Then for all i>=0 we have 3 3 3 13 a(i) + 55 b(i) + 55 c(i) = -228488 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 318, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 30 (19999437117654518848721480622049640418647400587 t / ----- i = 0 / + 33323294063443482770674542887940276696568086806 t - 1) / ((t - 1) / 2 (t - 100934039509918583531545702793807126406920402498 t + 1)) infinity ----- \ i 2 ) b(i) t = - (375494411061231660859508966645322269331333645313 t / ----- i = 0 / + 421197878817852355654577948226452190802961313214 t + 1) / ((t - 1) / 2 (t - 100934039509918583531545702793807126406920402498 t + 1)) infinity ----- \ i 2 ) c(i) t = 2 (77224000406735594686819985148176279720510135207 t / ----- i = 0 / - 475570145346277602943863442584063509787657614482 t + 11) / ((t - 1) / 2 (t - 100934039509918583531545702793807126406920402498 t + 1)) In Maple notation, these generating functions are 30*(19999437117654518848721480622049640418647400587*t^2+ 33323294063443482770674542887940276696568086806*t-1)/(t-1)/(t^2-\ 100934039509918583531545702793807126406920402498*t+1) -(375494411061231660859508966645322269331333645313*t^2+ 421197878817852355654577948226452190802961313214*t+1)/(t-1)/(t^2-\ 100934039509918583531545702793807126406920402498*t+1) 2*(77224000406735594686819985148176279720510135207*t^2-\ 475570145346277602943863442584063509787657614482*t+11)/(t-1)/(t^2-\ 100934039509918583531545702793807126406920402498*t+1) Then for all i>=0 we have 3 3 3 13 a(i) + 57 b(i) + 57 c(i) = -255879 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 319, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (7243797558415851576422208581723739612678273270668061667 t / ----- i = 0 / + 15834359192966640143297968143534018168387942320850478138 t - 29) / ( / (t - 1) 2 (t - 2412386955169188232702916633909850858227199745546801154 t + 1)) infinity ----- \ i ) b(i) t = - 16 ( / ----- i = 0 2 366438968979369836275420012067002846630190988805034065 t / - 97245574840318788849343477810967986913851103035863122 t + 1) / ( / (t - 1) 2 (t - 2412386955169188232702916633909850858227199745546801154 t + 1)) infinity ----- \ i ) c(i) t = 22 ( / ----- i = 0 2 225343127675815269697906550925299004295375984638501697 t / - 421120141595125122371416757656960720452714083379716930 t + 1) / ( / (t - 1) 2 (t - 2412386955169188232702916633909850858227199745546801154 t + 1)) In Maple notation, these generating functions are (7243797558415851576422208581723739612678273270668061667*t^2+ 15834359192966640143297968143534018168387942320850478138*t-29)/(t-1)/(t^2-\ 2412386955169188232702916633909850858227199745546801154*t+1) -16*(366438968979369836275420012067002846630190988805034065*t^2-\ 97245574840318788849343477810967986913851103035863122*t+1)/(t-1)/(t^2-\ 2412386955169188232702916633909850858227199745546801154*t+1) 22*(225343127675815269697906550925299004295375984638501697*t^2-\ 421120141595125122371416757656960720452714083379716930*t+1)/(t-1)/(t^2-\ 2412386955169188232702916633909850858227199745546801154*t+1) Then for all i>=0 we have 3 3 3 13 a(i) + 62 b(i) + 62 c(i) = -89167 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 320, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 2 (33083631759979772686483838718647151369830048397486707 t / ----- i = 0 / + 46128006829335902579246443916354738500516461631313306 t - 13) / ( / 2 (t - 1) (t - 11108267435113445284323587870696735614759181171097602 t + 1)) infinity ----- \ i ) b(i) t = - 2 ( / ----- i = 0 2 20201355264907484239276642670801862126520712914674561 t / + 16142808323131472647352545832316652049285332863245438 t + 1) / ( / 2 (t - 1) (t - 11108267435113445284323587870696735614759181171097602 t + 1)) infinity ----- \ i 2 ) c(i) t = (18346956023161786687564059529172290006488060231024659 t / ----- i = 0 / - 91035283199239700460822436535409318358100151786864678 t + 19) / ( / 2 (t - 1) (t - 11108267435113445284323587870696735614759181171097602 t + 1)) In Maple notation, these generating functions are 2*(33083631759979772686483838718647151369830048397486707*t^2+ 46128006829335902579246443916354738500516461631313306*t-13)/(t-1)/(t^2-\ 11108267435113445284323587870696735614759181171097602*t+1) -2*(20201355264907484239276642670801862126520712914674561*t^2+ 16142808323131472647352545832316652049285332863245438*t+1)/(t-1)/(t^2-\ 11108267435113445284323587870696735614759181171097602*t+1) (18346956023161786687564059529172290006488060231024659*t^2-\ 91035283199239700460822436535409318358100151786864678*t+19)/(t-1)/(t^2-\ 11108267435113445284323587870696735614759181171097602*t+1) Then for all i>=0 we have 3 3 3 13 a(i) + 63 b(i) + 63 c(i) = -203125 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 321, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 30 ( / ----- i = 0 9026782324842321874051175147942361351600789404011049012909024502733662527 2 t + 23488780775134563007184484111449276204985485018635504627343815452902157314 / 2 t - 1) / ((t - 1) (t - / 105789349293340919567276671806871472081895615877347007260471737328556910402 t + 1)) infinity ----- \ i ) b(i) t = - 11 ( / ----- i = 0 17041726381958601562488224340006167901289330280890944561362620332751761001 2 t + 7500959813604833937353109781915158441083192319719646971842576859717832598 t / 2 + 1) / ((t - 1) (t - / 105789349293340919567276671806871472081895615877347007260471737328556910402 t + 1)) infinity ----- \ i ) c(i) t = 20 ( / ----- i = 0 6834166981215327832291630376644603215571409634611911973868778041619625965 2 t - 20332644388775217357204364143701332703876297064947737317131636497477902446 / 2 t + 1) / ((t - 1) (t - / 105789349293340919567276671806871472081895615877347007260471737328556910402 t + 1)) In Maple notation, these generating functions are 30*(9026782324842321874051175147942361351600789404011049012909024502733662527*t ^2+23488780775134563007184484111449276204985485018635504627343815452902157314*t -1)/(t-1)/(t^2-\ 105789349293340919567276671806871472081895615877347007260471737328556910402*t+1 ) -11*(17041726381958601562488224340006167901289330280890944561362620332751761001 *t^2+7500959813604833937353109781915158441083192319719646971842576859717832598* t+1)/(t-1)/(t^2-\ 105789349293340919567276671806871472081895615877347007260471737328556910402*t+1 ) 20*(6834166981215327832291630376644603215571409634611911973868778041619625965*t ^2-20332644388775217357204364143701332703876297064947737317131636497477902446*t +1)/(t-1)/(t^2-\ 105789349293340919567276671806871472081895615877347007260471737328556910402*t+1 ) Then for all i>=0 we have 3 3 3 13 a(i) + 64 b(i) + 64 c(i) = -75816 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 322, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 2 (1103128227141143880979790890974707 t / ----- i = 0 / + 7192093041269487767407457392058906 t - 13) / ((t - 1) / 2 (t - 4144300490043938876209431305011202 t + 1)) infinity ----- \ i 2 ) b(i) t = - (2360928790066552161336862163660183 t / ----- i = 0 / - 897845070737941152323628428185006 t + 23) / ((t - 1) / 2 (t - 4144300490043938876209431305011202 t + 1)) infinity ----- \ i 2 ) c(i) t = 5 (446229799727636458597259705885573 t / ----- i = 0 / - 738846543593358660399906452980618 t + 5) / ((t - 1) / 2 (t - 4144300490043938876209431305011202 t + 1)) In Maple notation, these generating functions are 2*(1103128227141143880979790890974707*t^2+7192093041269487767407457392058906*t-\ 13)/(t-1)/(t^2-4144300490043938876209431305011202*t+1) -(2360928790066552161336862163660183*t^2-897845070737941152323628428185006*t+23 )/(t-1)/(t^2-4144300490043938876209431305011202*t+1) 5*(446229799727636458597259705885573*t^2-738846543593358660399906452980618*t+5) /(t-1)/(t^2-4144300490043938876209431305011202*t+1) Then for all i>=0 we have 3 3 3 13 a(i) + 68 b(i) + 68 c(i) = -6656 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 323, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 2 (1208991156169238200771317353367841523 t / ----- i = 0 / + 2993043937481065837228881900450501914 t - 13) / ((t - 1) / 2 (t - 1030562404297147351091821019528232962 t + 1)) infinity ----- \ i 2 ) b(i) t = - 2 (824930218685673263555578707069307141 t / ----- i = 0 / + 212280975316616973672318577101043446 t + 5) / ((t - 1) / 2 (t - 1030562404297147351091821019528232962 t + 1)) infinity ----- \ i 2 ) c(i) t = (1246863385314933793520718296349333777 t / ----- i = 0 / - 3321285773319514267976512864690034978 t + 17) / ((t - 1) / 2 (t - 1030562404297147351091821019528232962 t + 1)) In Maple notation, these generating functions are 2*(1208991156169238200771317353367841523*t^2+ 2993043937481065837228881900450501914*t-13)/(t-1)/(t^2-\ 1030562404297147351091821019528232962*t+1) -2*(824930218685673263555578707069307141*t^2+ 212280975316616973672318577101043446*t+5)/(t-1)/(t^2-\ 1030562404297147351091821019528232962*t+1) (1246863385314933793520718296349333777*t^2-\ 3321285773319514267976512864690034978*t+17)/(t-1)/(t^2-\ 1030562404297147351091821019528232962*t+1) Then for all i>=0 we have 3 3 3 13 a(i) + 72 b(i) + 72 c(i) = -53248 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 324, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 9 (442400998982730055292938640338657242285450058045437 t / ----- i = 0 / + 30909259356578728909620001618241342495819224460072966 t - 3) / ( / 2 (t - 1) (t - 563452787946069298767801486436670765687229276450508802 t + 1) ) infinity ----- \ i 2 ) b(i) t = - (3746369515686682123826131497005463157080738233949143 t / ----- i = 0 / + 26454263739531976070888795244562064104711095591535634 t + 23) / ( / 2 (t - 1) (t - 563452787946069298767801486436670765687229276450508802 t + 1) ) infinity ----- \ i 2 ) c(i) t = 5 (692393774696699703370419902786122414550875496469701 t / ----- i = 0 / - 6732520425740431342313405251099627866909242261566666 t + 5) / ((t - 1) / 2 (t - 563452787946069298767801486436670765687229276450508802 t + 1)) In Maple notation, these generating functions are 9*(442400998982730055292938640338657242285450058045437*t^2+ 30909259356578728909620001618241342495819224460072966*t-3)/(t-1)/(t^2-\ 563452787946069298767801486436670765687229276450508802*t+1) -(3746369515686682123826131497005463157080738233949143*t^2+ 26454263739531976070888795244562064104711095591535634*t+23)/(t-1)/(t^2-\ 563452787946069298767801486436670765687229276450508802*t+1) 5*(692393774696699703370419902786122414550875496469701*t^2-\ 6732520425740431342313405251099627866909242261566666*t+5)/(t-1)/(t^2-\ 563452787946069298767801486436670765687229276450508802*t+1) Then for all i>=0 we have 3 3 3 13 a(i) + 74 b(i) + 74 c(i) = -13 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 325, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 30 (701496946147568106720305855 t + 5490177536978128736562778946 t - 1) ------------------------------------------------------------------------ 2 (t - 1) (t - 46407886062021996148057881602 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 9 (2495079407061515430634707043 t - 866385480190325739164076646 t + 3) - ----------------------------------------------------------------------- 2 (t - 1) (t - 46407886062021996148057881602 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 21348087906478531338785564669 t - 36006333248319238562021238298 t + 29 ----------------------------------------------------------------------- 2 (t - 1) (t - 46407886062021996148057881602 t + 1) In Maple notation, these generating functions are 30*(701496946147568106720305855*t^2+5490177536978128736562778946*t-1)/(t-1)/(t^ 2-46407886062021996148057881602*t+1) -9*(2495079407061515430634707043*t^2-866385480190325739164076646*t+3)/(t-1)/(t^ 2-46407886062021996148057881602*t+1) (21348087906478531338785564669*t^2-36006333248319238562021238298*t+29)/(t-1)/(t ^2-46407886062021996148057881602*t+1) Then for all i>=0 we have 3 3 3 13 a(i) + 76 b(i) + 76 c(i) = -6656 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 326, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 9 (248801938109292474850796097377439 t / ----- i = 0 / + 1663976026333361022785900286649762 t - 1) / ((t - 1) / 2 (t - 10649402259700173820938403437844802 t + 1)) infinity ----- \ i 2 ) b(i) t = - 2 (642081401161546461390275956311841 t / ----- i = 0 / + 2430619127531228722456316404299358 t + 1) / ((t - 1) / 2 (t - 10649402259700173820938403437844802 t + 1)) infinity ----- \ i 2 ) c(i) t = 5 (144871688315436970873252138704889 t / ----- i = 0 / - 1373951899792547044411889082949370 t + 1) / ((t - 1) / 2 (t - 10649402259700173820938403437844802 t + 1)) In Maple notation, these generating functions are 9*(248801938109292474850796097377439*t^2+1663976026333361022785900286649762*t-1 )/(t-1)/(t^2-10649402259700173820938403437844802*t+1) -2*(642081401161546461390275956311841*t^2+2430619127531228722456316404299358*t+ 1)/(t-1)/(t^2-10649402259700173820938403437844802*t+1) 5*(144871688315436970873252138704889*t^2-1373951899792547044411889082949370*t+1 )/(t-1)/(t^2-10649402259700173820938403437844802*t+1) Then for all i>=0 we have 3 3 3 13 a(i) + 84 b(i) + 84 c(i) = -351 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 327, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 2 (32084031204216608333684550118557052403 t / ----- i = 0 / + 63188534558796019738955954088120399386 t - 13) / ((t - 1) / 2 (t - 21161589916855998418422533346192417794 t + 1)) infinity ----- \ i 2 ) b(i) t = - (68241294334201959328170229212671598935 t / ----- i = 0 / - 55253709106260295062786442652562089326 t + 23) / ((t - 1) / 2 (t - 21161589916855998418422533346192417794 t + 1)) infinity ----- \ i 2 ) c(i) t = (65324564224727722206926179201893685081 t / ----- i = 0 / - 78312149452669386472309965762003194738 t + 25) / ((t - 1) / 2 (t - 21161589916855998418422533346192417794 t + 1)) In Maple notation, these generating functions are 2*(32084031204216608333684550118557052403*t^2+ 63188534558796019738955954088120399386*t-13)/(t-1)/(t^2-\ 21161589916855998418422533346192417794*t+1) -(68241294334201959328170229212671598935*t^2-\ 55253709106260295062786442652562089326*t+23)/(t-1)/(t^2-\ 21161589916855998418422533346192417794*t+1) (65324564224727722206926179201893685081*t^2-\ 78312149452669386472309965762003194738*t+25)/(t-1)/(t^2-\ 21161589916855998418422533346192417794*t+1) Then for all i>=0 we have 3 3 3 13 a(i) + 88 b(i) + 88 c(i) = -75816 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 328, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 8 (369101 t + 438038 t - 3) ) a(i) t = ---------------------------- / 2 ----- (t - 1) (t - 586754 t + 1) i = 0 infinity ----- 2 \ i 3137359 t - 2716390 t + 23 ) b(i) t = - --------------------------- / 2 ----- (t - 1) (t - 586754 t + 1) i = 0 infinity ----- 2 \ i 3008977 t - 3429994 t + 25 ) c(i) t = --------------------------- / 2 ----- (t - 1) (t - 586754 t + 1) i = 0 In Maple notation, these generating functions are 8*(369101*t^2+438038*t-3)/(t-1)/(t^2-586754*t+1) -(3137359*t^2-2716390*t+23)/(t-1)/(t^2-586754*t+1) (3008977*t^2-3429994*t+25)/(t-1)/(t^2-586754*t+1) Then for all i>=0 we have 3 3 3 13 a(i) + 92 b(i) + 92 c(i) = -138424 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 329, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 2 (133249332748788294846804473274948634758708461515950540\ / ----- i = 0 2 408726614006526760101282191795 t + 904114781114240983054395263439263638\ / 2 5654695868139457566268786777028439727235575055962 t - 13) / ((t - 1) (t / - 364288158761217679541819163150574607599026497323378230224192963597403\ 53621950255349762 t + 1)) infinity ----- \ i ) b(i) t = - 3 (6239061034889189696294623291227040567043416411508264\ / ----- i = 0 2 7816655217062747462933821464581 t + 95200957787155558831415433246537090\ / 2 5454185435730262523216202618896702288855511310326 t + 5) / ((t - 1) (t / - 364288158761217679541819163150574607599026497323378230224192963597403\ 53621950255349762 t + 1)) infinity ----- \ i ) c(i) t = 6 (262601447022686042278877655941000682145241760754690816\ / ----- i = 0 2 70967363568169036648344725187 t - 5334602388124923468664380482829207237\ / 2 76833975998141667187396281547893912543011112646 t + 3) / ((t - 1) (t - / 364288158761217679541819163150574607599026497323378230224192963597403536\ 21950255349762 t + 1)) In Maple notation, these generating functions are 2*(1332493327487882948468044732749486347587084615159505404087266140065267601012\ 82191795*t^2+904114781114240983054395263439263638565469586813945756626878677702\ 8439727235575055962*t-13)/(t-1)/(t^2-364288158761217679541819163150574607599026\ 49732337823022419296359740353621950255349762*t+1) -3*(623906103488918969629462329122704056704341641150826478166552170627474629338\ 21464581*t^2+952009577871555588314154332465370905454185435730262523216202618896\ 702288855511310326*t+5)/(t-1)/(t^2-36428815876121767954181916315057460759902649\ 732337823022419296359740353621950255349762*t+1) 6*(2626014470226860422788776559410006821452417607546908167096736356816903664834\ 4725187*t^2-5334602388124923468664380482829207237768339759981416671873962815478\ 93912543011112646*t+3)/(t-1)/(t^2-364288158761217679541819163150574607599026497\ 32337823022419296359740353621950255349762*t+1) Then for all i>=0 we have 3 3 3 13 a(i) + 93 b(i) + 93 c(i) = -13 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 330, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 18 / ----- i = 0 2 (22259417070722680884903452959 t + 132901867702932402041334526242 t - 1) / 2 / ((t - 1) (t - 920969248763914537559794401602 t + 1)) / infinity ----- \ i ) b(i) t = - 8 / ----- i = 0 2 (33172472019327951832797522451 t + 31817517187775788151820055948 t + 1) / 2 / ((t - 1) (t - 920969248763914537559794401602 t + 1)) / infinity ----- \ i ) c(i) t = / ----- i = 0 2 215296087745497582671347410451 t - 735216001402327502548288037662 t + 11 ------------------------------------------------------------------------- 2 (t - 1) (t - 920969248763914537559794401602 t + 1) In Maple notation, these generating functions are 18*(22259417070722680884903452959*t^2+132901867702932402041334526242*t-1)/(t-1) /(t^2-920969248763914537559794401602*t+1) -8*(33172472019327951832797522451*t^2+31817517187775788151820055948*t+1)/(t-1)/ (t^2-920969248763914537559794401602*t+1) (215296087745497582671347410451*t^2-735216001402327502548288037662*t+11)/(t-1)/ (t^2-920969248763914537559794401602*t+1) Then for all i>=0 we have 3 3 3 13 a(i) + 96 b(i) + 96 c(i) = -2808 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 331, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 14 (5421453119507405550223590489352799 t / ----- i = 0 / + 6980469467468322816987226371741602 t - 1) / ((t - 1) / 2 (t - 21797318486199765009037193271014402 t + 1)) infinity ----- \ i 2 ) b(i) t = - (40038324781715663945198217420459601 t / ----- i = 0 / + 28360157364635322807297802843757998 t + 1) / ((t - 1) / 2 (t - 21797318486199765009037193271014402 t + 1)) infinity ----- \ i 2 ) c(i) t = 9 (2039168033742893527144872829227601 t / ----- i = 0 / - 9638999383337447610755541747474002 t + 1) / ((t - 1) / 2 (t - 21797318486199765009037193271014402 t + 1)) In Maple notation, these generating functions are 14*(5421453119507405550223590489352799*t^2+6980469467468322816987226371741602*t -1)/(t-1)/(t^2-21797318486199765009037193271014402*t+1) -(40038324781715663945198217420459601*t^2+28360157364635322807297802843757998*t +1)/(t-1)/(t^2-21797318486199765009037193271014402*t+1) 9*(2039168033742893527144872829227601*t^2-9638999383337447610755541747474002*t+ 1)/(t-1)/(t^2-21797318486199765009037193271014402*t+1) Then for all i>=0 we have 3 3 3 13 a(i) + 98 b(i) + 98 c(i) = -35672 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 332, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 9 (3829753007836757 t + 5192604280737646 t - 3) ) a(i) t = ------------------------------------------------ / 2 ----- (t - 1) (t - 6502873789598402 t + 1) i = 0 infinity ----- 2 \ i 36276737795082613 t + 5594471595658174 t + 13 ) b(i) t = - ---------------------------------------------- / 2 ----- (t - 1) (t - 6502873789598402 t + 1) i = 0 infinity ----- 2 \ i 24111640005483511 t - 65982849396224342 t + 31 ) c(i) t = ----------------------------------------------- / 2 ----- (t - 1) (t - 6502873789598402 t + 1) i = 0 In Maple notation, these generating functions are 9*(3829753007836757*t^2+5192604280737646*t-3)/(t-1)/(t^2-6502873789598402*t+1) -(36276737795082613*t^2+5594471595658174*t+13)/(t-1)/(t^2-6502873789598402*t+1) (24111640005483511*t^2-65982849396224342*t+31)/(t-1)/(t^2-6502873789598402*t+1) Then for all i>=0 we have 3 3 3 14 a(i) + 17 b(i) + 17 c(i) = -193536 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 333, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 24 ( / ----- i = 0 2 33031181434759071523337126366060975983240425409861607671257783371 t + 43216252947339184314586381119503488506574335169197007110174802262 t - 1) / 2 / ((t - 1) (t / - 158020595837662449202935085777728532087099545096999672066424534274 t + 1 )) infinity ----- \ i ) b(i) t = - 9 ( / ----- i = 0 2 82009529147260916056572404049153242612482023006610474032168904345 t + 20529437685568688244388679366568010598566174984334444619342628198 t + 1) / 2 / ((t - 1) (t / - 158020595837662449202935085777728532087099545096999672066424534274 t + 1 )) infinity ----- \ i ) c(i) t = ( / ----- i = 0 2 462347204261272517009989538082217992695722481898910410946846469233 t - 1385197905756738955718639288823709271595156263817414678810450262154 t / 2 + 25) / ((t - 1) (t / - 158020595837662449202935085777728532087099545096999672066424534274 t + 1 )) In Maple notation, these generating functions are 24*(33031181434759071523337126366060975983240425409861607671257783371*t^2+ 43216252947339184314586381119503488506574335169197007110174802262*t-1)/(t-1)/(t ^2-158020595837662449202935085777728532087099545096999672066424534274*t+1) -9*(82009529147260916056572404049153242612482023006610474032168904345*t^2+ 20529437685568688244388679366568010598566174984334444619342628198*t+1)/(t-1)/(t ^2-158020595837662449202935085777728532087099545096999672066424534274*t+1) (462347204261272517009989538082217992695722481898910410946846469233*t^2-\ 1385197905756738955718639288823709271595156263817414678810450262154*t+25)/(t-1) /(t^2-158020595837662449202935085777728532087099545096999672066424534274*t+1) Then for all i>=0 we have 3 3 3 14 a(i) + 23 b(i) + 23 c(i) = -149072 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 334, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 25 (303666454066121502179284335192409532755438079 t / ----- i = 0 / + 1023244052273943979737609638173787073028753922 t - 1) / ((t - 1) / 2 (t - 3756915289035125159644217876398267498304640002 t + 1)) infinity ----- \ i 2 ) b(i) t = - 2 (3202607266418450335800423599339690221869170401 t / ----- i = 0 / + 7988204232835113969522778585676425730527629598 t + 1) / ((t - 1) / 2 (t - 3756915289035125159644217876398267498304640002 t + 1)) infinity ----- \ i 2 ) c(i) t = 22 (118608357136835540652717864035193694740698401 t / ----- i = 0 / - 1135954857068977750227554426309386054049498402 t + 1) / ((t - 1) / 2 (t - 3756915289035125159644217876398267498304640002 t + 1)) In Maple notation, these generating functions are 25*(303666454066121502179284335192409532755438079*t^2+ 1023244052273943979737609638173787073028753922*t-1)/(t-1)/(t^2-\ 3756915289035125159644217876398267498304640002*t+1) -2*(3202607266418450335800423599339690221869170401*t^2+ 7988204232835113969522778585676425730527629598*t+1)/(t-1)/(t^2-\ 3756915289035125159644217876398267498304640002*t+1) 22*(118608357136835540652717864035193694740698401*t^2-\ 1135954857068977750227554426309386054049498402*t+1)/(t-1)/(t^2-\ 3756915289035125159644217876398267498304640002*t+1) Then for all i>=0 we have 3 3 3 14 a(i) + 25 b(i) + 25 c(i) = -47250 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 335, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 8 (403 t + 5860 t - 3) ) a(i) t = -------------------------- / 2 ----- (t - 1) (t - 16898 t + 1) i = 0 infinity ----- 2 \ i 5 (517 t + 5978 t + 1) ) b(i) t = - -------------------------- / 2 ----- (t - 1) (t - 16898 t + 1) i = 0 infinity ----- 2 \ i 1031 t - 33530 t + 19 ) c(i) t = -------------------------- / 2 ----- (t - 1) (t - 16898 t + 1) i = 0 In Maple notation, these generating functions are 8*(403*t^2+5860*t-3)/(t-1)/(t^2-16898*t+1) -5*(517*t^2+5978*t+1)/(t-1)/(t^2-16898*t+1) (1031*t^2-33530*t+19)/(t-1)/(t^2-16898*t+1) Then for all i>=0 we have 3 3 3 14 a(i) + 29 b(i) + 29 c(i) = -1750 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 336, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 3 (51844604526737071442007843548090823572121135593 t / ----- i = 0 / + 142310476771896038477981139962351910866313524414 t - 7) / ((t - 1) / 2 (t - 96053275859347212645059028184533216803070840002 t + 1)) infinity ----- \ i 2 ) b(i) t = - (151064234102968149039127654014398213623128354613 t / ----- i = 0 / + 6672543552310567460933735871576950463431105374 t + 13) / ((t - 1) / 2 (t - 96053275859347212645059028184533216803070840002 t + 1)) infinity ----- \ i 2 ) c(i) t = (122785358906566110070759739351803218947425917019 t / ----- i = 0 / - 280522136561844826570821129237778383033985377038 t + 19) / ((t - 1) / 2 (t - 96053275859347212645059028184533216803070840002 t + 1)) In Maple notation, these generating functions are 3*(51844604526737071442007843548090823572121135593*t^2+ 142310476771896038477981139962351910866313524414*t-7)/(t-1)/(t^2-\ 96053275859347212645059028184533216803070840002*t+1) -(151064234102968149039127654014398213623128354613*t^2+ 6672543552310567460933735871576950463431105374*t+13)/(t-1)/(t^2-\ 96053275859347212645059028184533216803070840002*t+1) (122785358906566110070759739351803218947425917019*t^2-\ 280522136561844826570821129237778383033985377038*t+19)/(t-1)/(t^2-\ 96053275859347212645059028184533216803070840002*t+1) Then for all i>=0 we have 3 3 3 14 a(i) + 33 b(i) + 33 c(i) = -24192 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 337, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 4 (2749798 t + 4582273 t - 5) ) a(i) t = ------------------------------ / 2 ----- (t - 1) (t - 3104642 t + 1) i = 0 infinity ----- 2 \ i 3 (2772211 t + 2405716 t + 1) ) b(i) t = - ------------------------------ / 2 ----- (t - 1) (t - 3104642 t + 1) i = 0 infinity ----- 2 \ i 17 (244399 t - 1158152 t + 1) ) c(i) t = ------------------------------ / 2 ----- (t - 1) (t - 3104642 t + 1) i = 0 In Maple notation, these generating functions are 4*(2749798*t^2+4582273*t-5)/(t-1)/(t^2-3104642*t+1) -3*(2772211*t^2+2405716*t+1)/(t-1)/(t^2-3104642*t+1) 17*(244399*t^2-1158152*t+1)/(t-1)/(t^2-3104642*t+1) Then for all i>=0 we have 3 3 3 14 a(i) + 37 b(i) + 37 c(i) = -68782 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 338, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = ( / ----- i = 0 2 1498462195214733913299461779421 t + 6631847539819446217440604641398 t - 19 / 2 ) / ((t - 1) (t - 1986676727379515932352233948802 t + 1)) / infinity ----- \ i ) b(i) t = - 3 / ----- i = 0 2 (420618869958713811323131057283 t + 469148669080927210512348128314 t + 3) / 2 / ((t - 1) (t - 1986676727379515932352233948802 t + 1)) / infinity ----- \ i ) c(i) t = 15 / ----- i = 0 2 (61924334062635593178708259169 t - 239877841870563797545804096290 t + 1) / 2 / ((t - 1) (t - 1986676727379515932352233948802 t + 1)) / In Maple notation, these generating functions are (1498462195214733913299461779421*t^2+6631847539819446217440604641398*t-19)/(t-1 )/(t^2-1986676727379515932352233948802*t+1) -3*(420618869958713811323131057283*t^2+469148669080927210512348128314*t+3)/(t-1 )/(t^2-1986676727379515932352233948802*t+1) 15*(61924334062635593178708259169*t^2-239877841870563797545804096290*t+1)/(t-1) /(t^2-1986676727379515932352233948802*t+1) Then for all i>=0 we have 3 3 3 14 a(i) + 39 b(i) + 39 c(i) = -7168 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 339, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 618845315401291 t + 3145436197349938 t - 29 ) a(i) t = -------------------------------------------- / 2 ----- (t - 1) (t - 575539388121602 t + 1) i = 0 infinity ----- 2 \ i 7 (65385875490001 t + 194876421344398 t + 1) ) b(i) t = - --------------------------------------------- / 2 ----- (t - 1) (t - 575539388121602 t + 1) i = 0 infinity ----- 2 \ i 21 (11732766376321 t - 98486865321122 t + 1) ) c(i) t = --------------------------------------------- / 2 ----- (t - 1) (t - 575539388121602 t + 1) i = 0 In Maple notation, these generating functions are (618845315401291*t^2+3145436197349938*t-29)/(t-1)/(t^2-575539388121602*t+1) -7*(65385875490001*t^2+194876421344398*t+1)/(t-1)/(t^2-575539388121602*t+1) 21*(11732766376321*t^2-98486865321122*t+1)/(t-1)/(t^2-575539388121602*t+1) Then for all i>=0 we have 3 3 3 14 a(i) + 41 b(i) + 41 c(i) = -24192 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 340, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (16815103744105491476023693982557 t / ----- i = 0 / + 106697132869298701910959433184430 t - 27) / ((t - 1) / 2 (t - 21856580599027903738729957502498 t + 1)) infinity ----- \ i ) b(i) t = - 5 ( / ----- i = 0 2 2399480120022524773631336630461 t + 10544013383900624498909089938962 t + 1 / 2 ) / ((t - 1) (t - 21856580599027903738729957502498 t + 1)) / infinity ----- \ i 2 ) c(i) t = (5634928913153789255607177321071 t / ----- i = 0 / - 70352396432769535618309310168210 t + 19) / ((t - 1) / 2 (t - 21856580599027903738729957502498 t + 1)) In Maple notation, these generating functions are (16815103744105491476023693982557*t^2+106697132869298701910959433184430*t-27)/( t-1)/(t^2-21856580599027903738729957502498*t+1) -5*(2399480120022524773631336630461*t^2+10544013383900624498909089938962*t+1)/( t-1)/(t^2-21856580599027903738729957502498*t+1) (5634928913153789255607177321071*t^2-70352396432769535618309310168210*t+19)/(t-\ 1)/(t^2-21856580599027903738729957502498*t+1) Then for all i>=0 we have 3 3 3 14 a(i) + 43 b(i) + 43 c(i) = -14000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 341, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 4 (210727856283641536952513 t + 15721685452245220797185798 t - 7) ------------------------------------------------------------------ 2 (t - 1) (t - 44991378470026373880782594 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 3 (191024670487848240841081 t + 13472300678327102612324998 t + 1) - ------------------------------------------------------------------ 2 (t - 1) (t - 44991378470026373880782594 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 123521251391776110357883 t - 41113497297836628669856142 t + 19 --------------------------------------------------------------- 2 (t - 1) (t - 44991378470026373880782594 t + 1) In Maple notation, these generating functions are 4*(210727856283641536952513*t^2+15721685452245220797185798*t-7)/(t-1)/(t^2-\ 44991378470026373880782594*t+1) -3*(191024670487848240841081*t^2+13472300678327102612324998*t+1)/(t-1)/(t^2-\ 44991378470026373880782594*t+1) (123521251391776110357883*t^2-41113497297836628669856142*t+19)/(t-1)/(t^2-\ 44991378470026373880782594*t+1) Then for all i>=0 we have 3 3 3 14 a(i) + 45 b(i) + 45 c(i) = -112 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 342, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 18 (41831612549 t + 300210697152 t - 1) ) a(i) t = ---------------------------------------- / 2 ----- (t - 1) (t - 1417761727202 t + 1) i = 0 infinity ----- 2 \ i 457518837931 t + 2758699895068 t + 1 ) b(i) t = - ------------------------------------- / 2 ----- (t - 1) (t - 1417761727202 t + 1) i = 0 infinity ----- 2 \ i 156331227581 t - 3372549960592 t + 11 ) c(i) t = -------------------------------------- / 2 ----- (t - 1) (t - 1417761727202 t + 1) i = 0 In Maple notation, these generating functions are 18*(41831612549*t^2+300210697152*t-1)/(t-1)/(t^2-1417761727202*t+1) -(457518837931*t^2+2758699895068*t+1)/(t-1)/(t^2-1417761727202*t+1) (156331227581*t^2-3372549960592*t+11)/(t-1)/(t^2-1417761727202*t+1) Then for all i>=0 we have 3 3 3 14 a(i) + 65 b(i) + 65 c(i) = -4802 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 343, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 2 ( / ----- i = 0 2 14491115407201181043406887344576549746335397649593458893701883 t + 1066170406116189206623294367975132962935058904933667180037137026 t - 13) / / ((t - 1) ( / 2 t - 4094622214280344747370144291285116020823433886135099868439026562 t + 1 )) infinity ----- \ i ) b(i) t = - 3 ( / ----- i = 0 2 5622089909961435175951381053077800457595199858940052055718767 t + 226079586287339510109365167166349423475227855374453323733196206 t + 3) / / ((t - 1) ( / 2 t - 4094622214280344747370144291285116020823433886135099868439026562 t + 1 )) infinity ----- \ i ) c(i) t = 3 ( / ----- i = 0 2 3475257997783482428779990335362756050730696503444724812207377 t - 235176934195084427714096538554789979983553751736838100601122358 t + 5) / / ((t - 1) ( / 2 t - 4094622214280344747370144291285116020823433886135099868439026562 t + 1 )) In Maple notation, these generating functions are 2*(14491115407201181043406887344576549746335397649593458893701883*t^2+ 1066170406116189206623294367975132962935058904933667180037137026*t-13)/(t-1)/(t ^2-4094622214280344747370144291285116020823433886135099868439026562*t+1) -3*(5622089909961435175951381053077800457595199858940052055718767*t^2+ 226079586287339510109365167166349423475227855374453323733196206*t+3)/(t-1)/(t^2 -4094622214280344747370144291285116020823433886135099868439026562*t+1) 3*(3475257997783482428779990335362756050730696503444724812207377*t^2-\ 235176934195084427714096538554789979983553751736838100601122358*t+5)/(t-1)/(t^2 -4094622214280344747370144291285116020823433886135099868439026562*t+1) Then for all i>=0 we have 3 3 3 14 a(i) + 93 b(i) + 93 c(i) = -14 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 344, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 17 (74108571342733507487146843225331654083451762147955959\ / ----- i = 0 2 55179246974319568796972077283804132799 t + 9623108597704420777092506113\ 7938605845445427743027283116294371104010247314243065638991801154 t - 1) / 2 / ((t - 1) (t - 1168650983020104856779828195876495987696906722933564\ / 654758764365158373165864118213284468335874 t + 1)) infinity ----- \ i ) b(i) t = - 2 (4726197163822920879502045762547507289063577347878610\ / ----- i = 0 2 1312228596802320886710976320316650739829 t + 84434677910588617834313548\ 885962628969493237423305971400055018267847272576098981421872657286 t + 5) / 2 / ((t - 1) (t - 1168650983020104856779828195876495987696906722933564\ / 654758764365158373165864118213284468335874 t + 1)) infinity ----- \ i ) c(i) t = 12 (68271238456828101097688293252203137155903956160349741\ / ----- i = 0 2 25054372812358208872258342437569537825 t - 2877656543715244788132449707\ 7126597358945230766383652910434975324052902086770892727323437346 t + 1) / 2 / ((t - 1) (t - 1168650983020104856779828195876495987696906722933564\ / 654758764365158373165864118213284468335874 t + 1)) In Maple notation, these generating functions are 17*(741085713427335074871468432253316540834517621479559595517924697431956879697\ 2077283804132799*t^2+9623108597704420777092506113793860584544542774302728311629\ 4371104010247314243065638991801154*t-1)/(t-1)/(t^2-1168650983020104856779828195\ 876495987696906722933564654758764365158373165864118213284468335874*t+1) -2*(472619716382292087950204576254750728906357734787861013122285968023208867109\ 76320316650739829*t^2+844346779105886178343135488859626289694932374233059714000\ 55018267847272576098981421872657286*t+5)/(t-1)/(t^2-116865098302010485677982819\ 5876495987696906722933564654758764365158373165864118213284468335874*t+1) 12*(682712384568281010976882932522031371559039561603497412505437281235820887225\ 8342437569537825*t^2-2877656543715244788132449707712659735894523076638365291043\ 4975324052902086770892727323437346*t+1)/(t-1)/(t^2-1168650983020104856779828195\ 876495987696906722933564654758764365158373165864118213284468335874*t+1) Then for all i>=0 we have 3 3 3 14 a(i) + 95 b(i) + 95 c(i) = -378 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 345, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 50735235130805888755 t + 867966073144243221706 t - 29 ) a(i) t = ------------------------------------------------------ / 2 ----- (t - 1) (t - 458808754034334396482 t + 1) i = 0 infinity ----- 2 \ i 23 (2011865115718636089 t + 1616509488250252838 t + 1) ) b(i) t = - ------------------------------------------------------- / 2 ----- (t - 1) (t - 458808754034334396482 t + 1) i = 0 infinity ----- 2 \ i 43198034926328273153 t - 126650650817612718522 t + 25 ) c(i) t = ------------------------------------------------------ / 2 ----- (t - 1) (t - 458808754034334396482 t + 1) i = 0 In Maple notation, these generating functions are (50735235130805888755*t^2+867966073144243221706*t-29)/(t-1)/(t^2-\ 458808754034334396482*t+1) -23*(2011865115718636089*t^2+1616509488250252838*t+1)/(t-1)/(t^2-\ 458808754034334396482*t+1) (43198034926328273153*t^2-126650650817612718522*t+25)/(t-1)/(t^2-\ 458808754034334396482*t+1) Then for all i>=0 we have 3 3 3 14 a(i) + 99 b(i) + 99 c(i) = -896 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 346, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 28 / ----- i = 0 2 (11715610809398298281366372855 t + 17753630535323099374177602314 t - 1) / 2 / ((t - 1) (t - 70221537498987112726723716098 t + 1)) / infinity ----- \ i ) b(i) t = / ----- i = 0 2 6 (62515557191154310781824222387 t - 2705897384073361588935085750 t + 3) - ------------------------------------------------------------------------- 2 (t - 1) (t - 70221537498987112726723716098 t + 1) infinity ----- \ i ) c(i) t = 3 / ----- i = 0 2 (92870614121215253732446636939 t - 212489933735377152118224910230 t + 11) / 2 / ((t - 1) (t - 70221537498987112726723716098 t + 1)) / In Maple notation, these generating functions are 28*(11715610809398298281366372855*t^2+17753630535323099374177602314*t-1)/(t-1)/ (t^2-70221537498987112726723716098*t+1) -6*(62515557191154310781824222387*t^2-2705897384073361588935085750*t+3)/(t-1)/( t^2-70221537498987112726723716098*t+1) 3*(92870614121215253732446636939*t^2-212489933735377152118224910230*t+11)/(t-1) /(t^2-70221537498987112726723716098*t+1) Then for all i>=0 we have 3 3 3 15 a(i) + 17 b(i) + 17 c(i) = -182505 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 347, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 26 (360280279316854058108266867583646276043602455 t / ----- i = 0 / + 1082735711461969285189896853406601860119566314 t - 1) / ((t - 1) / 2 (t - 4138492961014971806269302615175402080163884098 t + 1)) infinity ----- \ i 2 ) b(i) t = - 3 (2085241601753561666329979474110403030107421929 t / ----- i = 0 / + 4089419299227923799506990679970125828396419350 t + 1) / ((t - 1) / 2 (t - 4138492961014971806269302615175402080163884098 t + 1)) infinity ----- \ i 2 ) c(i) t = 18 (161681392708168898538827163201440124519219849 t / ----- i = 0 / - 1190791542871749809511655522214861600936526730 t + 1) / ((t - 1) / 2 (t - 4138492961014971806269302615175402080163884098 t + 1)) In Maple notation, these generating functions are 26*(360280279316854058108266867583646276043602455*t^2+ 1082735711461969285189896853406601860119566314*t-1)/(t-1)/(t^2-\ 4138492961014971806269302615175402080163884098*t+1) -3*(2085241601753561666329979474110403030107421929*t^2+ 4089419299227923799506990679970125828396419350*t+1)/(t-1)/(t^2-\ 4138492961014971806269302615175402080163884098*t+1) 18*(161681392708168898538827163201440124519219849*t^2-\ 1190791542871749809511655522214861600936526730*t+1)/(t-1)/(t^2-\ 4138492961014971806269302615175402080163884098*t+1) Then for all i>=0 we have 3 3 3 15 a(i) + 56 b(i) + 56 c(i) = -61440 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 348, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 4 (994960219788077 t + 4373222704308926 t - 3) ) a(i) t = ----------------------------------------------- / 2 ----- (t - 1) (t - 8500545331353602 t + 1) i = 0 infinity ----- 2 \ i 10 (505578335584981 t + 247074115628618 t + 1) ) b(i) t = - ----------------------------------------------- / 2 ----- (t - 1) (t - 8500545331353602 t + 1) i = 0 infinity ----- 2 \ i 14 (294239300558141 t - 831848194282142 t + 1) ) c(i) t = ----------------------------------------------- / 2 ----- (t - 1) (t - 8500545331353602 t + 1) i = 0 In Maple notation, these generating functions are 4*(994960219788077*t^2+4373222704308926*t-3)/(t-1)/(t^2-8500545331353602*t+1) -10*(505578335584981*t^2+247074115628618*t+1)/(t-1)/(t^2-8500545331353602*t+1) 14*(294239300558141*t^2-831848194282142*t+1)/(t-1)/(t^2-8500545331353602*t+1) Then for all i>=0 we have 3 3 3 16 a(i) + 17 b(i) + 17 c(i) = -2000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 349, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 9 (1135105845760017037 t + 4455630296762942966 t - 3) ) a(i) t = ------------------------------------------------------ / 2 ----- (t - 1) (t - 5611066092132134402 t + 1) i = 0 infinity ----- 2 \ i 2 (4758848549570991721 t + 14452953831098816278 t + 1) ) b(i) t = - ------------------------------------------------------- / 2 ----- (t - 1) (t - 5611066092132134402 t + 1) i = 0 infinity ----- 2 \ i 26 (141538842014468521 t - 1619369794373684522 t + 1) ) c(i) t = ------------------------------------------------------ / 2 ----- (t - 1) (t - 5611066092132134402 t + 1) i = 0 In Maple notation, these generating functions are 9*(1135105845760017037*t^2+4455630296762942966*t-3)/(t-1)/(t^2-\ 5611066092132134402*t+1) -2*(4758848549570991721*t^2+14452953831098816278*t+1)/(t-1)/(t^2-\ 5611066092132134402*t+1) 26*(141538842014468521*t^2-1619369794373684522*t+1)/(t-1)/(t^2-\ 5611066092132134402*t+1) Then for all i>=0 we have 3 3 3 16 a(i) + 21 b(i) + 21 c(i) = -54000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 350, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 109628548042606364381 t + 1156661626480451533238 t - 19 ) a(i) t = -------------------------------------------------------- / 2 ----- (t - 1) (t - 629567996373045734402 t + 1) i = 0 infinity ----- 2 \ i 18 (7555630863370585601 t + 10727278122210287998 t + 1) ) b(i) t = - -------------------------------------------------------- / 2 ----- (t - 1) (t - 629567996373045734402 t + 1) i = 0 infinity ----- 2 \ i 2 (58467760549239064811 t - 223013941419466927222 t + 11) ) c(i) t = ---------------------------------------------------------- / 2 ----- (t - 1) (t - 629567996373045734402 t + 1) i = 0 In Maple notation, these generating functions are (109628548042606364381*t^2+1156661626480451533238*t-19)/(t-1)/(t^2-\ 629567996373045734402*t+1) -18*(7555630863370585601*t^2+10727278122210287998*t+1)/(t-1)/(t^2-\ 629567996373045734402*t+1) 2*(58467760549239064811*t^2-223013941419466927222*t+11)/(t-1)/(t^2-\ 629567996373045734402*t+1) Then for all i>=0 we have 3 3 3 16 a(i) + 23 b(i) + 23 c(i) = -1024 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 351, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 3 (4799815047388593184560064602976818137 t / ----- i = 0 / + 9740224561489795204478903821580653550 t - 7) / ((t - 1) / 2 (t - 5551651487026293748542151580285580098 t + 1)) infinity ----- \ i 2 ) b(i) t = - 8 (1674708176489679608218524606158745409 t / ----- i = 0 / + 968935388760936462515833289215340350 t + 1) / ((t - 1) / 2 (t - 5551651487026293748542151580285580098 t + 1)) infinity ----- \ i 2 ) c(i) t = 20 (429892518226442184059406612314657257 t / ----- i = 0 / - 1487349944326688612353149770464291562 t + 1) / ((t - 1) / 2 (t - 5551651487026293748542151580285580098 t + 1)) In Maple notation, these generating functions are 3*(4799815047388593184560064602976818137*t^2+ 9740224561489795204478903821580653550*t-7)/(t-1)/(t^2-\ 5551651487026293748542151580285580098*t+1) -8*(1674708176489679608218524606158745409*t^2+ 968935388760936462515833289215340350*t+1)/(t-1)/(t^2-\ 5551651487026293748542151580285580098*t+1) 20*(429892518226442184059406612314657257*t^2-\ 1487349944326688612353149770464291562*t+1)/(t-1)/(t^2-\ 5551651487026293748542151580285580098*t+1) Then for all i>=0 we have 3 3 3 16 a(i) + 27 b(i) + 27 c(i) = -54000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 352, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 808243647841 t + 9933666844918 t - 23 ) a(i) t = -------------------------------------- / 2 ----- (t - 1) (t - 2871160802498 t + 1) i = 0 infinity ----- 2 \ i 3 (223832180353 t + 2348018422654 t + 1) ) b(i) t = - ----------------------------------------- / 2 ----- (t - 1) (t - 2871160802498 t + 1) i = 0 infinity ----- 2 \ i 225569011219 t - 7941120820262 t + 19 ) c(i) t = -------------------------------------- / 2 ----- (t - 1) (t - 2871160802498 t + 1) i = 0 In Maple notation, these generating functions are (808243647841*t^2+9933666844918*t-23)/(t-1)/(t^2-2871160802498*t+1) -3*(223832180353*t^2+2348018422654*t+1)/(t-1)/(t^2-2871160802498*t+1) (225569011219*t^2-7941120820262*t+19)/(t-1)/(t^2-2871160802498*t+1) Then for all i>=0 we have 3 3 3 16 a(i) + 29 b(i) + 29 c(i) = -3456 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 353, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (58763 t + 986690 t - 13) ) a(i) t = ---------------------------- / 2 ----- (t - 1) (t - 688898 t + 1) i = 0 infinity ----- 2 \ i 5 (19177 t + 266518 t + 1) ) b(i) t = - --------------------------- / 2 ----- (t - 1) (t - 688898 t + 1) i = 0 infinity ----- 2 \ i 3 (11743 t - 487910 t + 7) ) c(i) t = --------------------------- / 2 ----- (t - 1) (t - 688898 t + 1) i = 0 In Maple notation, these generating functions are 2*(58763*t^2+986690*t-13)/(t-1)/(t^2-688898*t+1) -5*(19177*t^2+266518*t+1)/(t-1)/(t^2-688898*t+1) 3*(11743*t^2-487910*t+7)/(t-1)/(t^2-688898*t+1) Then for all i>=0 we have 3 3 3 16 a(i) + 31 b(i) + 31 c(i) = -2000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 354, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 9 (4195941213049354724381 t + 46737640749599881168678 t - 3) ------------------------------------------------------------- 2 (t - 1) (t - 141972346573053775638914 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 2 (15863839633768244372909 t + 103248552830065008069902 t + 5) - --------------------------------------------------------------- 2 (t - 1) (t - 141972346573053775638914 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 2 (8997754012414754823923 t - 128110146476248007266750 t + 11) --------------------------------------------------------------- 2 (t - 1) (t - 141972346573053775638914 t + 1) In Maple notation, these generating functions are 9*(4195941213049354724381*t^2+46737640749599881168678*t-3)/(t-1)/(t^2-\ 141972346573053775638914*t+1) -2*(15863839633768244372909*t^2+103248552830065008069902*t+5)/(t-1)/(t^2-\ 141972346573053775638914*t+1) 2*(8997754012414754823923*t^2-128110146476248007266750*t+11)/(t-1)/(t^2-\ 141972346573053775638914*t+1) Then for all i>=0 we have 3 3 3 16 a(i) + 33 b(i) + 33 c(i) = -3456 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 355, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 8 (399552743822907847 t + 1510571656690442056 t - 3) ) a(i) t = ----------------------------------------------------- / 2 ----- (t - 1) (t - 2771569701389452802 t + 1) i = 0 infinity ----- 2 \ i 22 (176002546754785661 t - 57123944366757662 t + 1) ) b(i) t = - ---------------------------------------------------- / 2 ----- (t - 1) (t - 2771569701389452802 t + 1) i = 0 infinity ----- 2 \ i 2 (1753375331412170113 t - 3061039957680478126 t + 13) ) c(i) t = ------------------------------------------------------- / 2 ----- (t - 1) (t - 2771569701389452802 t + 1) i = 0 In Maple notation, these generating functions are 8*(399552743822907847*t^2+1510571656690442056*t-3)/(t-1)/(t^2-\ 2771569701389452802*t+1) -22*(176002546754785661*t^2-57123944366757662*t+1)/(t-1)/(t^2-\ 2771569701389452802*t+1) 2*(1753375331412170113*t^2-3061039957680478126*t+13)/(t-1)/(t^2-\ 2771569701389452802*t+1) Then for all i>=0 we have 3 3 3 16 a(i) + 35 b(i) + 35 c(i) = -21296 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 356, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (1136159429 t + 13457371034 t - 15) ) a(i) t = -------------------------------------- / 2 ----- (t - 1) (t - 7269608642 t + 1) i = 0 infinity ----- 2 \ i 7 (253171885 t + 2220166226 t + 1) ) b(i) t = - ----------------------------------- / 2 ----- (t - 1) (t - 7269608642 t + 1) i = 0 infinity ----- 2 \ i 789578827 t - 18102945634 t + 23 ) c(i) t = --------------------------------- / 2 ----- (t - 1) (t - 7269608642 t + 1) i = 0 In Maple notation, these generating functions are 2*(1136159429*t^2+13457371034*t-15)/(t-1)/(t^2-7269608642*t+1) -7*(253171885*t^2+2220166226*t+1)/(t-1)/(t^2-7269608642*t+1) (789578827*t^2-18102945634*t+23)/(t-1)/(t^2-7269608642*t+1) Then for all i>=0 we have 3 3 3 16 a(i) + 37 b(i) + 37 c(i) = -5488 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 357, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 4 (57165953956557305 t + 211840461145391798 t - 7) ) a(i) t = --------------------------------------------------- / 2 ----- (t - 1) (t - 165247324784962562 t + 1) i = 0 infinity ----- 2 \ i 26 (10581308306885749 t - 4532075881721942 t + 1) ) b(i) t = - -------------------------------------------------- / 2 ----- (t - 1) (t - 165247324784962562 t + 1) i = 0 infinity ----- 2 \ i 6 (42134225170062161 t - 68347565679105334 t + 5) ) c(i) t = -------------------------------------------------- / 2 ----- (t - 1) (t - 165247324784962562 t + 1) i = 0 In Maple notation, these generating functions are 4*(57165953956557305*t^2+211840461145391798*t-7)/(t-1)/(t^2-165247324784962562* t+1) -26*(10581308306885749*t^2-4532075881721942*t+1)/(t-1)/(t^2-165247324784962562* t+1) 6*(42134225170062161*t^2-68347565679105334*t+5)/(t-1)/(t^2-165247324784962562*t +1) Then for all i>=0 we have 3 3 3 16 a(i) + 41 b(i) + 41 c(i) = -35152 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 358, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 4 (1549486051108246673 t + 4629771305191924334 t - 7) ) a(i) t = ------------------------------------------------------ / 2 ----- (t - 1) (t - 3290262587989977602 t + 1) i = 0 infinity ----- 2 \ i 26 (286273477478677261 t - 153767273104705262 t + 1) ) b(i) t = - ----------------------------------------------------- / 2 ----- (t - 1) (t - 3290262587989977602 t + 1) i = 0 infinity ----- 2 \ i 30 (228885248839867621 t - 343723959297310022 t + 1) ) c(i) t = ----------------------------------------------------- / 2 ----- (t - 1) (t - 3290262587989977602 t + 1) i = 0 In Maple notation, these generating functions are 4*(1549486051108246673*t^2+4629771305191924334*t-7)/(t-1)/(t^2-\ 3290262587989977602*t+1) -26*(286273477478677261*t^2-153767273104705262*t+1)/(t-1)/(t^2-\ 3290262587989977602*t+1) 30*(228885248839867621*t^2-343723959297310022*t+1)/(t-1)/(t^2-\ 3290262587989977602*t+1) Then for all i>=0 we have 3 3 3 16 a(i) + 43 b(i) + 43 c(i) = -54000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 359, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 151252099005487409983 t + 269342169466499799634 t - 17 ) a(i) t = ------------------------------------------------------- / 2 ----- (t - 1) (t - 62185765967886220802 t + 1) i = 0 infinity ----- 2 \ i 2 (60163595908638724043 t + 21770352494995147954 t + 3) ) b(i) t = - -------------------------------------------------------- / 2 ----- (t - 1) (t - 62185765967886220802 t + 1) i = 0 infinity ----- 2 \ i 14 (5713807053510533721 t - 17418656825458229722 t + 1) ) c(i) t = -------------------------------------------------------- / 2 ----- (t - 1) (t - 62185765967886220802 t + 1) i = 0 In Maple notation, these generating functions are (151252099005487409983*t^2+269342169466499799634*t-17)/(t-1)/(t^2-\ 62185765967886220802*t+1) -2*(60163595908638724043*t^2+21770352494995147954*t+3)/(t-1)/(t^2-\ 62185765967886220802*t+1) 14*(5713807053510533721*t^2-17418656825458229722*t+1)/(t-1)/(t^2-\ 62185765967886220802*t+1) Then for all i>=0 we have 3 3 3 16 a(i) + 45 b(i) + 45 c(i) = -35152 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 360, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 3 (38136586072640640131424481518130820231 t / ----- i = 0 / + 66952880425242792266788117241187243778 t - 9) / ((t - 1) / 2 (t - 31484062690274982189315253468191897602 t + 1)) infinity ----- \ i 2 ) b(i) t = - 26 (5267215535698886194725847690843556641 t / ----- i = 0 / - 3720653091674090873971440382100852642 t + 1) / ((t - 1) / 2 (t - 31484062690274982189315253468191897602 t + 1)) infinity ----- \ i 2 ) c(i) t = 30 (4240353440959114360551696524817912321 t / ----- i = 0 / - 5580707559113936971872182859061589122 t + 1) / ((t - 1) / 2 (t - 31484062690274982189315253468191897602 t + 1)) In Maple notation, these generating functions are 3*(38136586072640640131424481518130820231*t^2+ 66952880425242792266788117241187243778*t-9)/(t-1)/(t^2-\ 31484062690274982189315253468191897602*t+1) -26*(5267215535698886194725847690843556641*t^2-\ 3720653091674090873971440382100852642*t+1)/(t-1)/(t^2-\ 31484062690274982189315253468191897602*t+1) 30*(4240353440959114360551696524817912321*t^2-\ 5580707559113936971872182859061589122*t+1)/(t-1)/(t^2-\ 31484062690274982189315253468191897602*t+1) Then for all i>=0 we have 3 3 3 16 a(i) + 47 b(i) + 47 c(i) = -128000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 361, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (125701 t + 234586 t - 15) ) a(i) t = ----------------------------- / 2 ----- (t - 1) (t - 58562 t + 1) i = 0 infinity ----- 2 \ i 181435 t + 130622 t + 7 ) b(i) t = - -------------------------- / 2 ----- (t - 1) (t - 58562 t + 1) i = 0 infinity ----- 2 \ i 23 (4589 t - 18158 t + 1) ) c(i) t = -------------------------- / 2 ----- (t - 1) (t - 58562 t + 1) i = 0 In Maple notation, these generating functions are 2*(125701*t^2+234586*t-15)/(t-1)/(t^2-58562*t+1) -(181435*t^2+130622*t+7)/(t-1)/(t^2-58562*t+1) 23*(4589*t^2-18158*t+1)/(t-1)/(t^2-58562*t+1) Then for all i>=0 we have 3 3 3 16 a(i) + 53 b(i) + 53 c(i) = -194672 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 362, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (9750329115013694660761133533768176589352918705418140899 t / ----- i = 0 / + 25593986397291383962201595240323466083083883544673986362 t - 29) / ( / (t - 1) 2 (t - 3341184654970076415558561483498698975166483605655106562 t + 1)) infinity ----- \ i ) b(i) t = - 4 ( / ----- i = 0 2 1612088620486987218837277476087333839281698052652397601 t / + 2505695711043701552770030730602954627409968228911733726 t + 1) / ( / (t - 1) 2 (t - 3341184654970076415558561483498698975166483605655106562 t + 1)) infinity ----- \ i 2 ) c(i) t = 4 (799561194235845997107183014939985790168954827200885861 t / ----- i = 0 / - 4917345525766534768714491221630274256860621108765017194 t + 5) / ( / (t - 1) 2 (t - 3341184654970076415558561483498698975166483605655106562 t + 1)) In Maple notation, these generating functions are (9750329115013694660761133533768176589352918705418140899*t^2+ 25593986397291383962201595240323466083083883544673986362*t-29)/(t-1)/(t^2-\ 3341184654970076415558561483498698975166483605655106562*t+1) -4*(1612088620486987218837277476087333839281698052652397601*t^2+ 2505695711043701552770030730602954627409968228911733726*t+1)/(t-1)/(t^2-\ 3341184654970076415558561483498698975166483605655106562*t+1) 4*(799561194235845997107183014939985790168954827200885861*t^2-\ 4917345525766534768714491221630274256860621108765017194*t+5)/(t-1)/(t^2-\ 3341184654970076415558561483498698975166483605655106562*t+1) Then for all i>=0 we have 3 3 3 16 a(i) + 63 b(i) + 63 c(i) = -109744 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 363, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 39359746956703207872005977 t + 48027248050432877686434046 t - 23 ----------------------------------------------------------------- 2 (t - 1) (t - 7502294215370780526480002 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 6 (4478260187829382703806601 t + 1131461317621578565993398 t + 1) - ------------------------------------------------------------------ 2 (t - 1) (t - 7502294215370780526480002 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 6 (2728938100864795687273003 t - 8338659606315756957073006 t + 3) ------------------------------------------------------------------ 2 (t - 1) (t - 7502294215370780526480002 t + 1) In Maple notation, these generating functions are (39359746956703207872005977*t^2+48027248050432877686434046*t-23)/(t-1)/(t^2-\ 7502294215370780526480002*t+1) -6*(4478260187829382703806601*t^2+1131461317621578565993398*t+1)/(t-1)/(t^2-\ 7502294215370780526480002*t+1) 6*(2728938100864795687273003*t^2-8338659606315756957073006*t+3)/(t-1)/(t^2-\ 7502294215370780526480002*t+1) Then for all i>=0 we have 3 3 3 16 a(i) + 65 b(i) + 65 c(i) = -170368 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 364, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = ( / ----- i = 0 2 14955320337045479418354345954338671171782855189729466993934617 t + 19691635016470859296926874211421549427571343878874662855491966 t - 23) / / ((t - 1) / 2 (t - 3455951247828804193244610351411951035788974992792546647127042 t + 1)) infinity ----- \ i ) b(i) t = - 18 ( / ----- i = 0 2 806900916399068358077055656438186717956347741097909661769601 t / - 538771768310974242882809074541547851508973842068310016312322 t + 1) / / ((t - 1) 2 (t - 3455951247828804193244610351411951035788974992792546647127042 t + 1)) infinity ----- \ i ) c(i) t = 2 ( / ----- i = 0 2 6566511952845313854397949933323277151291648033149583839929451 t - 8979674285638160891146169170393026949318013124415980649044982 t + 11) / / ((t - 1) / 2 (t - 3455951247828804193244610351411951035788974992792546647127042 t + 1)) In Maple notation, these generating functions are (14955320337045479418354345954338671171782855189729466993934617*t^2+ 19691635016470859296926874211421549427571343878874662855491966*t-23)/(t-1)/(t^2 -3455951247828804193244610351411951035788974992792546647127042*t+1) -18*(806900916399068358077055656438186717956347741097909661769601*t^2-\ 538771768310974242882809074541547851508973842068310016312322*t+1)/(t-1)/(t^2-\ 3455951247828804193244610351411951035788974992792546647127042*t+1) 2*(6566511952845313854397949933323277151291648033149583839929451*t^2-\ 8979674285638160891146169170393026949318013124415980649044982*t+11)/(t-1)/(t^2-\ 3455951247828804193244610351411951035788974992792546647127042*t+1) Then for all i>=0 we have 3 3 3 16 a(i) + 67 b(i) + 67 c(i) = -128000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 365, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 3180589325737 t + 17677775754286 t - 23 ) a(i) t = ---------------------------------------- / 2 ----- (t - 1) (t - 3522746102402 t + 1) i = 0 infinity ----- 2 \ i 2 (962830744681 t + 4135880719318 t + 1) ) b(i) t = - ----------------------------------------- / 2 ----- (t - 1) (t - 3522746102402 t + 1) i = 0 infinity ----- 2 \ i 14 (54934539481 t - 783321891482 t + 1) ) c(i) t = ---------------------------------------- / 2 ----- (t - 1) (t - 3522746102402 t + 1) i = 0 In Maple notation, these generating functions are (3180589325737*t^2+17677775754286*t-23)/(t-1)/(t^2-3522746102402*t+1) -2*(962830744681*t^2+4135880719318*t+1)/(t-1)/(t^2-3522746102402*t+1) 14*(54934539481*t^2-783321891482*t+1)/(t-1)/(t^2-3522746102402*t+1) Then for all i>=0 we have 3 3 3 16 a(i) + 77 b(i) + 77 c(i) = -16000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 366, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 4197178941143911717735411 t + 5720976556864549787464618 t - 29 --------------------------------------------------------------- 2 (t - 1) (t - 783736695679362509145602 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 14 (221661289661313983183641 t - 65515401354475230623642 t + 1) - ---------------------------------------------------------------- 2 (t - 1) (t - 783736695679362509145602 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 2 (1240726883840759977268051 t - 2333748101988631245188062 t + 11) ------------------------------------------------------------------- 2 (t - 1) (t - 783736695679362509145602 t + 1) In Maple notation, these generating functions are (4197178941143911717735411*t^2+5720976556864549787464618*t-29)/(t-1)/(t^2-\ 783736695679362509145602*t+1) -14*(221661289661313983183641*t^2-65515401354475230623642*t+1)/(t-1)/(t^2-\ 783736695679362509145602*t+1) 2*(1240726883840759977268051*t^2-2333748101988631245188062*t+11)/(t-1)/(t^2-\ 783736695679362509145602*t+1) Then for all i>=0 we have 3 3 3 16 a(i) + 81 b(i) + 81 c(i) = -250000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 367, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (148212536361107389 t + 301855995068682622 t - 11) ) a(i) t = ----------------------------------------------------- / 2 ----- (t - 1) (t - 93746193624720002 t + 1) i = 0 infinity ----- 2 \ i 2 (86133380302347301 t + 105699108503792698 t + 1) ) b(i) t = - --------------------------------------------------- / 2 ----- (t - 1) (t - 93746193624720002 t + 1) i = 0 infinity ----- 2 \ i 2 (40529522960468107 t - 232362011766608114 t + 7) ) c(i) t = --------------------------------------------------- / 2 ----- (t - 1) (t - 93746193624720002 t + 1) i = 0 In Maple notation, these generating functions are 2*(148212536361107389*t^2+301855995068682622*t-11)/(t-1)/(t^2-93746193624720002 *t+1) -2*(86133380302347301*t^2+105699108503792698*t+1)/(t-1)/(t^2-93746193624720002* t+1) 2*(40529522960468107*t^2-232362011766608114*t+7)/(t-1)/(t^2-93746193624720002*t +1) Then for all i>=0 we have 3 3 3 16 a(i) + 91 b(i) + 91 c(i) = -78608 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 368, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 360781 t + 69916038 t - 19 ) a(i) t = ----------------------------- / 2 ----- (t - 1) (t - 84603202 t + 1) i = 0 infinity ----- 2 \ i 341881 t + 65482118 t + 1 ) b(i) t = - ----------------------------- / 2 ----- (t - 1) (t - 84603202 t + 1) i = 0 infinity ----- 2 \ i 2 (17609 t - 32929618 t + 9) ) c(i) t = ----------------------------- / 2 ----- (t - 1) (t - 84603202 t + 1) i = 0 In Maple notation, these generating functions are (360781*t^2+69916038*t-19)/(t-1)/(t^2-84603202*t+1) -(341881*t^2+65482118*t+1)/(t-1)/(t^2-84603202*t+1) 2*(17609*t^2-32929618*t+9)/(t-1)/(t^2-84603202*t+1) Then for all i>=0 we have 3 3 3 17 a(i) + 20 b(i) + 20 c(i) = -17 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 369, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 34262491307 t + 2129586814826 t - 21 ) a(i) t = ------------------------------------- / 2 ----- (t - 1) (t - 1467465732098 t + 1) i = 0 infinity ----- 2 \ i 2 (15521625601 t + 926644386302 t + 1) ) b(i) t = - --------------------------------------- / 2 ----- (t - 1) (t - 1467465732098 t + 1) i = 0 infinity ----- 2 \ i 5718801107 t - 1890050824934 t + 19 ) c(i) t = ------------------------------------ / 2 ----- (t - 1) (t - 1467465732098 t + 1) i = 0 In Maple notation, these generating functions are (34262491307*t^2+2129586814826*t-21)/(t-1)/(t^2-1467465732098*t+1) -2*(15521625601*t^2+926644386302*t+1)/(t-1)/(t^2-1467465732098*t+1) (5718801107*t^2-1890050824934*t+19)/(t-1)/(t^2-1467465732098*t+1) Then for all i>=0 we have 3 3 3 17 a(i) + 23 b(i) + 23 c(i) = -136 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 370, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 528911197160407753 t + 18183193678144892494 t - 23 ) a(i) t = --------------------------------------------------- / 2 ----- (t - 1) (t - 9179307997940747522 t + 1) i = 0 infinity ----- 2 \ i 3 (153833556961242001 t + 4886233691597528686 t + 1) ) b(i) t = - ----------------------------------------------------- / 2 ----- (t - 1) (t - 9179307997940747522 t + 1) i = 0 infinity ----- 2 \ i 4 (28918529723557157 t - 3808968966142635178 t + 5) ) c(i) t = ---------------------------------------------------- / 2 ----- (t - 1) (t - 9179307997940747522 t + 1) i = 0 In Maple notation, these generating functions are (528911197160407753*t^2+18183193678144892494*t-23)/(t-1)/(t^2-\ 9179307997940747522*t+1) -3*(153833556961242001*t^2+4886233691597528686*t+1)/(t-1)/(t^2-\ 9179307997940747522*t+1) 4*(28918529723557157*t^2-3808968966142635178*t+5)/(t-1)/(t^2-\ 9179307997940747522*t+1) Then for all i>=0 we have 3 3 3 17 a(i) + 26 b(i) + 26 c(i) = -459 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 371, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 30 (4619048849533503618258891209023518911 t / ----- i = 0 / + 6022608781447838503421439955202058050 t - 1) / ((t - 1) / 2 (t - 22916246615442318093116612337897062402 t + 1)) infinity ----- \ i 2 ) b(i) t = - 15 (9086255132800971796772419853104402945 t / ----- i = 0 / + 238775620584120885565295911135243774 t + 1) / ((t - 1) / 2 (t - 22916246615442318093116612337897062402 t + 1)) infinity ----- \ i 2 ) c(i) t = 32 (2967671724387469320684421303619665501 t / ----- i = 0 / - 7338779890036731515530225568106999902 t + 1) / ((t - 1) / 2 (t - 22916246615442318093116612337897062402 t + 1)) In Maple notation, these generating functions are 30*(4619048849533503618258891209023518911*t^2+ 6022608781447838503421439955202058050*t-1)/(t-1)/(t^2-\ 22916246615442318093116612337897062402*t+1) -15*(9086255132800971796772419853104402945*t^2+ 238775620584120885565295911135243774*t+1)/(t-1)/(t^2-\ 22916246615442318093116612337897062402*t+1) 32*(2967671724387469320684421303619665501*t^2-\ 7338779890036731515530225568106999902*t+1)/(t-1)/(t^2-\ 22916246615442318093116612337897062402*t+1) Then for all i>=0 we have 3 3 3 17 a(i) + 27 b(i) + 27 c(i) = -334611 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 372, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 9 (900272199726639413910736987061948918908131021777437 t / ----- i = 0 / + 106836461235956309048102173296670246775939922449548966 t - 3) / ( / (t - 1) 2 (t - 1486558061832258582898307377598314512810496324230369602 t + 1)) infinity ----- \ i 2 ) b(i) t = - 6 (1152810856577918249040096472478374069737573473448001 t / ----- i = 0 / + 123118639342255078846076572255445354082316562517710398 t + 1) / ( / (t - 1) 2 (t - 1486558061832258582898307377598314512810496324230369602 t + 1)) infinity ----- \ i 2 ) c(i) t = (1997520619532658411085480298424594968677439185975583 t / ----- i = 0 / - 747626221812530640981785492665966963881002255132926006 t + 23) / ( / (t - 1) 2 (t - 1486558061832258582898307377598314512810496324230369602 t + 1)) In Maple notation, these generating functions are 9*(900272199726639413910736987061948918908131021777437*t^2+ 106836461235956309048102173296670246775939922449548966*t-3)/(t-1)/(t^2-\ 1486558061832258582898307377598314512810496324230369602*t+1) -6*(1152810856577918249040096472478374069737573473448001*t^2+ 123118639342255078846076572255445354082316562517710398*t+1)/(t-1)/(t^2-\ 1486558061832258582898307377598314512810496324230369602*t+1) (1997520619532658411085480298424594968677439185975583*t^2-\ 747626221812530640981785492665966963881002255132926006*t+23)/(t-1)/(t^2-\ 1486558061832258582898307377598314512810496324230369602*t+1) Then for all i>=0 we have 3 3 3 17 a(i) + 28 b(i) + 28 c(i) = -17 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 373, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 1755751 t + 41301426 t - 25 ) a(i) t = ----------------------------- / 2 ----- (t - 1) (t - 16793602 t + 1) i = 0 infinity ----- 2 \ i 4 (370945 t + 7706366 t + 1) ) b(i) t = - ----------------------------- / 2 ----- (t - 1) (t - 16793602 t + 1) i = 0 infinity ----- 2 \ i 454549 t - 32763818 t + 21 ) c(i) t = ----------------------------- / 2 ----- (t - 1) (t - 16793602 t + 1) i = 0 In Maple notation, these generating functions are (1755751*t^2+41301426*t-25)/(t-1)/(t^2-16793602*t+1) -4*(370945*t^2+7706366*t+1)/(t-1)/(t^2-16793602*t+1) (454549*t^2-32763818*t+21)/(t-1)/(t^2-16793602*t+1) Then for all i>=0 we have 3 3 3 17 a(i) + 29 b(i) + 29 c(i) = -1088 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 374, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 27 (281637146111 t + 5065625257730 t - 1) ) a(i) t = ------------------------------------------ / 2 ----- (t - 1) (t - 47038062064898 t + 1) i = 0 infinity ----- 2 \ i 5 (1250488035217 t + 18913976711278 t + 1) ) b(i) t = - ------------------------------------------- / 2 ----- (t - 1) (t - 47038062064898 t + 1) i = 0 infinity ----- 2 \ i 2 (1106353680779 t - 51517515547030 t + 11) ) c(i) t = -------------------------------------------- / 2 ----- (t - 1) (t - 47038062064898 t + 1) i = 0 In Maple notation, these generating functions are 27*(281637146111*t^2+5065625257730*t-1)/(t-1)/(t^2-47038062064898*t+1) -5*(1250488035217*t^2+18913976711278*t+1)/(t-1)/(t^2-47038062064898*t+1) 2*(1106353680779*t^2-51517515547030*t+11)/(t-1)/(t^2-47038062064898*t+1) Then for all i>=0 we have 3 3 3 17 a(i) + 32 b(i) + 32 c(i) = -2125 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 375, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 5117437735414360086331 t + 75246367500977506646626 t - 29 ) a(i) t = ---------------------------------------------------------- / 2 ----- (t - 1) (t - 22548223557563763995714 t + 1) i = 0 infinity ----- \ i ) b(i) t = / ----- i = 0 2 6 (684817851887478647521 t + 8043999985946249119198 t + 1) - ----------------------------------------------------------- 2 (t - 1) (t - 22548223557563763995714 t + 1) infinity ----- 2 \ i 1623294496980754128911 t - 53996201523983120729254 t + 23 ) c(i) t = ---------------------------------------------------------- / 2 ----- (t - 1) (t - 22548223557563763995714 t + 1) i = 0 In Maple notation, these generating functions are (5117437735414360086331*t^2+75246367500977506646626*t-29)/(t-1)/(t^2-\ 22548223557563763995714*t+1) -6*(684817851887478647521*t^2+8043999985946249119198*t+1)/(t-1)/(t^2-\ 22548223557563763995714*t+1) (1623294496980754128911*t^2-53996201523983120729254*t+23)/(t-1)/(t^2-\ 22548223557563763995714*t+1) Then for all i>=0 we have 3 3 3 17 a(i) + 35 b(i) + 35 c(i) = -3672 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 376, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 9827124642651782874474245231 t + 45922163619285993630035068586 t - 25 ---------------------------------------------------------------------- 2 (t - 1) (t - 7960895226700562898603948098 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 3 (2593176594274759902515920441 t + 8991330282751623124024006342 t + 1) - ------------------------------------------------------------------------ 2 (t - 1) (t - 7960895226700562898603948098 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 4 (816091101617689461575709461 t - 9504471259387476731480654554 t + 5) ----------------------------------------------------------------------- 2 (t - 1) (t - 7960895226700562898603948098 t + 1) In Maple notation, these generating functions are (9827124642651782874474245231*t^2+45922163619285993630035068586*t-25)/(t-1)/(t^ 2-7960895226700562898603948098*t+1) -3*(2593176594274759902515920441*t^2+8991330282751623124024006342*t+1)/(t-1)/(t ^2-7960895226700562898603948098*t+1) 4*(816091101617689461575709461*t^2-9504471259387476731480654554*t+5)/(t-1)/(t^2 -7960895226700562898603948098*t+1) Then for all i>=0 we have 3 3 3 17 a(i) + 37 b(i) + 37 c(i) = -29376 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 377, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 25 (17313996709707983093053422717970920247644194335 t / ----- i = 0 / + 70639275877842049058214986401650438244270346466 t - 1) / ((t - 1) / 2 (t - 292123439316170931947174257789982321278622240002 t + 1)) infinity ----- \ i 2 ) b(i) t = - (340395507922192230034174614029044529227786190003 t / ----- i = 0 / + 1000912662322314870289701502384444554477992689994 t + 3) / ((t - 1) / 2 (t - 292123439316170931947174257789982321278622240002 t + 1)) infinity ----- \ i 2 ) c(i) t = 20 (7337606183443963061514382471007961849219858721 t / ----- i = 0 / - 74403014695669318077708188291682416034508802722 t + 1) / ((t - 1) / 2 (t - 292123439316170931947174257789982321278622240002 t + 1)) In Maple notation, these generating functions are 25*(17313996709707983093053422717970920247644194335*t^2+ 70639275877842049058214986401650438244270346466*t-1)/(t-1)/(t^2-\ 292123439316170931947174257789982321278622240002*t+1) -(340395507922192230034174614029044529227786190003*t^2+ 1000912662322314870289701502384444554477992689994*t+3)/(t-1)/(t^2-\ 292123439316170931947174257789982321278622240002*t+1) 20*(7337606183443963061514382471007961849219858721*t^2-\ 74403014695669318077708188291682416034508802722*t+1)/(t-1)/(t^2-\ 292123439316170931947174257789982321278622240002*t+1) Then for all i>=0 we have 3 3 3 17 a(i) + 38 b(i) + 38 c(i) = -37349 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 378, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 3 (135742412608545593 t + 212392323746928014 t - 7) ) a(i) t = ---------------------------------------------------- / 2 ----- (t - 1) (t - 96277837438036802 t + 1) i = 0 infinity ----- 2 \ i 2 (158139409423413601 t + 147189422117930398 t + 1) ) b(i) t = - ---------------------------------------------------- / 2 ----- (t - 1) (t - 96277837438036802 t + 1) i = 0 infinity ----- 2 \ i 19 (7537223303733241 t - 39677100308085242 t + 1) ) c(i) t = -------------------------------------------------- / 2 ----- (t - 1) (t - 96277837438036802 t + 1) i = 0 In Maple notation, these generating functions are 3*(135742412608545593*t^2+212392323746928014*t-7)/(t-1)/(t^2-96277837438036802* t+1) -2*(158139409423413601*t^2+147189422117930398*t+1)/(t-1)/(t^2-96277837438036802 *t+1) 19*(7537223303733241*t^2-39677100308085242*t+1)/(t-1)/(t^2-96277837438036802*t+ 1) Then for all i>=0 we have 3 3 3 17 a(i) + 40 b(i) + 40 c(i) = -116603 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 379, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (392978432557610871559229027767214999513 t / ----- i = 0 / + 639683762918826410501662694655496711230 t - 23) / ((t - 1) / 2 (t - 92038252109995482362763449601933936898 t + 1)) infinity ----- \ i 2 ) b(i) t = - (300091007372256132055047200559044577107 t / ----- i = 0 / + 267912051238184540019077591834486092970 t + 3) / ((t - 1) / 2 (t - 92038252109995482362763449601933936898 t + 1)) infinity ----- \ i 2 ) c(i) t = 20 (7236372050613521932395507153484025377 t / ----- i = 0 / - 35636524981135555536101746773160558882 t + 1) / ((t - 1) / 2 (t - 92038252109995482362763449601933936898 t + 1)) In Maple notation, these generating functions are (392978432557610871559229027767214999513*t^2+ 639683762918826410501662694655496711230*t-23)/(t-1)/(t^2-\ 92038252109995482362763449601933936898*t+1) -(300091007372256132055047200559044577107*t^2+ 267912051238184540019077591834486092970*t+3)/(t-1)/(t^2-\ 92038252109995482362763449601933936898*t+1) 20*(7236372050613521932395507153484025377*t^2-\ 35636524981135555536101746773160558882*t+1)/(t-1)/(t^2-\ 92038252109995482362763449601933936898*t+1) Then for all i>=0 we have 3 3 3 17 a(i) + 43 b(i) + 43 c(i) = -136000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 380, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 25 / ----- i = 0 2 (17277717538630171387026645263 t + 29151206813258698403347552946 t - 1) / 2 / ((t - 1) (t - 99945349368737297515380360002 t + 1)) / infinity ----- \ i ) b(i) t = - 4 / ----- i = 0 2 (81225851395727286434654778241 t + 69352362121098759418333870558 t + 1) / 2 / ((t - 1) (t - 99945349368737297515380360002 t + 1)) / infinity ----- \ i ) c(i) t = 21 / ----- i = 0 2 (7870110458484469839016723561 t - 36551674937879907144347894762 t + 1) / 2 / ((t - 1) (t - 99945349368737297515380360002 t + 1)) / In Maple notation, these generating functions are 25*(17277717538630171387026645263*t^2+29151206813258698403347552946*t-1)/(t-1)/ (t^2-99945349368737297515380360002*t+1) -4*(81225851395727286434654778241*t^2+69352362121098759418333870558*t+1)/(t-1)/ (t^2-99945349368737297515380360002*t+1) 21*(7870110458484469839016723561*t^2-36551674937879907144347894762*t+1)/(t-1)/( t^2-99945349368737297515380360002*t+1) Then for all i>=0 we have 3 3 3 17 a(i) + 46 b(i) + 46 c(i) = -157437 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 381, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 26794184840485975086631885 t + 46706010613770054798970318 t - 27 ----------------------------------------------------------------- 2 (t - 1) (t - 6112875847363394567814722 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 19883069661581306712458477 t + 16195694518380551210173582 t + 5 - ---------------------------------------------------------------- 2 (t - 1) (t - 6112875847363394567814722 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 22 (481233090101319529163009 t - 2121176916463222162009922 t + 1) ------------------------------------------------------------------ 2 (t - 1) (t - 6112875847363394567814722 t + 1) In Maple notation, these generating functions are (26794184840485975086631885*t^2+46706010613770054798970318*t-27)/(t-1)/(t^2-\ 6112875847363394567814722*t+1) -(19883069661581306712458477*t^2+16195694518380551210173582*t+5)/(t-1)/(t^2-\ 6112875847363394567814722*t+1) 22*(481233090101319529163009*t^2-2121176916463222162009922*t+1)/(t-1)/(t^2-\ 6112875847363394567814722*t+1) Then for all i>=0 we have 3 3 3 17 a(i) + 49 b(i) + 49 c(i) = -181016 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 382, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 657310064514143011 t + 1180374499702157818 t - 29 ) a(i) t = -------------------------------------------------- / 2 ----- (t - 1) (t - 147639149571513602 t + 1) i = 0 infinity ----- 2 \ i 6 (80306449345362241 t + 62269744683706558 t + 1) ) b(i) t = - -------------------------------------------------- / 2 ----- (t - 1) (t - 147639149571513602 t + 1) i = 0 infinity ----- 2 \ i 23 (11606472490813201 t - 48800262237526802 t + 1) ) c(i) t = --------------------------------------------------- / 2 ----- (t - 1) (t - 147639149571513602 t + 1) i = 0 In Maple notation, these generating functions are (657310064514143011*t^2+1180374499702157818*t-29)/(t-1)/(t^2-147639149571513602 *t+1) -6*(80306449345362241*t^2+62269744683706558*t+1)/(t-1)/(t^2-147639149571513602* t+1) 23*(11606472490813201*t^2-48800262237526802*t+1)/(t-1)/(t^2-147639149571513602* t+1) Then for all i>=0 we have 3 3 3 17 a(i) + 52 b(i) + 52 c(i) = -206839 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 383, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = ( / ----- i = 0 2 1694758269614689829007246715528324971156316470295425953533061533514059 t + 14558368404829403215755764191752205422377229349768140314407563746450770 t / 2 - 29) / ((t - 1) (t / - 2601889880846061616590440305781751991509372172352300338888147056492098 t + 1)) infinity ----- \ i ) b(i) t = - 2 ( / ----- i = 0 2 554549759869278615188706846652721760969796880831426399945991643032289 t + 4052017119678029439819921598261809362406251505328648498553852134936030 t / 2 + 1) / ((t - 1) (t / - 2601889880846061616590440305781751991509372172352300338888147056492098 t + 1)) infinity ----- \ i ) c(i) t = ( / ----- i = 0 2 370358735547538586963998458331558278102225043841769691941674412481531 t - 9583492494642154696981255348160620524854321816161919488941361968418190 t / 2 + 19) / ((t - 1) (t / - 2601889880846061616590440305781751991509372172352300338888147056492098 t + 1)) In Maple notation, these generating functions are (1694758269614689829007246715528324971156316470295425953533061533514059*t^2+ 14558368404829403215755764191752205422377229349768140314407563746450770*t-29)/( t-1)/(t^2-\ 2601889880846061616590440305781751991509372172352300338888147056492098*t+1) -2*(554549759869278615188706846652721760969796880831426399945991643032289*t^2+ 4052017119678029439819921598261809362406251505328648498553852134936030*t+1)/(t-\ 1)/(t^2-2601889880846061616590440305781751991509372172352300338888147056492098* t+1) (370358735547538586963998458331558278102225043841769691941674412481531*t^2-\ 9583492494642154696981255348160620524854321816161919488941361968418190*t+19)/(t -1)/(t^2-2601889880846061616590440305781751991509372172352300338888147056492098 *t+1) Then for all i>=0 we have 3 3 3 17 a(i) + 63 b(i) + 63 c(i) = -17000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 384, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 28 ( / ----- i = 0 2 19320297396427341702893734418503441259302768465414229792639 t / + 93968275772954626550624992563324701257808072129127937042562 t - 1) / ( / (t - 1) 2 (t - 369454937809309580320593240868731402993594535113176712806402 t + 1)) infinity ----- \ i ) b(i) t = - ( / ----- i = 0 2 339499332131309125027833127648294708670497769424644124160001 t + 1349258239621565839317120507710137074074981510098428840857598 t + 1) / / ((t - 1) / 2 (t - 369454937809309580320593240868731402993594535113176712806402 t + 1)) infinity ----- \ i ) c(i) t = 2 ( / ----- i = 0 2 60267980819232959530852068785961187199199863408308093255049 t / - 904646766695670441703328886465177078571939503169844575763858 t + 9) / / ((t - 1) 2 (t - 369454937809309580320593240868731402993594535113176712806402 t + 1)) In Maple notation, these generating functions are 28*(19320297396427341702893734418503441259302768465414229792639*t^2+ 93968275772954626550624992563324701257808072129127937042562*t-1)/(t-1)/(t^2-\ 369454937809309580320593240868731402993594535113176712806402*t+1) -(339499332131309125027833127648294708670497769424644124160001*t^2+ 1349258239621565839317120507710137074074981510098428840857598*t+1)/(t-1)/(t^2-\ 369454937809309580320593240868731402993594535113176712806402*t+1) 2*(60267980819232959530852068785961187199199863408308093255049*t^2-\ 904646766695670441703328886465177078571939503169844575763858*t+9)/(t-1)/(t^2-\ 369454937809309580320593240868731402993594535113176712806402*t+1) Then for all i>=0 we have 3 3 3 17 a(i) + 72 b(i) + 72 c(i) = -46648 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 385, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (66649986690060859603555354804273586462059 t / ----- i = 0 / + 177684820364432739669710363534693628944530 t - 29) / ((t - 1) / 2 (t - 28261706104598929789497035260318143002498 t + 1)) infinity ----- \ i 2 ) b(i) t = - (75154205890004871427854881873965306037887 t / ----- i = 0 / + 19382812914257138010586246530083691325006 t + 19) / ((t - 1) / 2 (t - 28261706104598929789497035260318143002498 t + 1)) infinity ----- \ i 2 ) c(i) t = (57767252840423777618231745838067848699963 t / ----- i = 0 / - 152304271644685787056672874242116846062906 t + 31) / ((t - 1) / 2 (t - 28261706104598929789497035260318143002498 t + 1)) In Maple notation, these generating functions are (66649986690060859603555354804273586462059*t^2+ 177684820364432739669710363534693628944530*t-29)/(t-1)/(t^2-\ 28261706104598929789497035260318143002498*t+1) -(75154205890004871427854881873965306037887*t^2+ 19382812914257138010586246530083691325006*t+19)/(t-1)/(t^2-\ 28261706104598929789497035260318143002498*t+1) (57767252840423777618231745838067848699963*t^2-\ 152304271644685787056672874242116846062906*t+31)/(t-1)/(t^2-\ 28261706104598929789497035260318143002498*t+1) Then for all i>=0 we have 3 3 3 18 a(i) + 23 b(i) + 23 c(i) = -88434 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 386, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 3 (1235673347040021919391 t + 1728535082062341752266 t - 9) ) a(i) t = ------------------------------------------------------------ / 2 ----- (t - 1) (t - 762242531345002495874 t + 1) i = 0 infinity ----- 2 \ i 4142954896038016561375 t - 972050475048958750994 t + 19 ) b(i) t = - -------------------------------------------------------- / 2 ----- (t - 1) (t - 762242531345002495874 t + 1) i = 0 infinity ----- 2 \ i 3253270086169200779419 t - 6424174507158258589850 t + 31 ) c(i) t = --------------------------------------------------------- / 2 ----- (t - 1) (t - 762242531345002495874 t + 1) i = 0 In Maple notation, these generating functions are 3*(1235673347040021919391*t^2+1728535082062341752266*t-9)/(t-1)/(t^2-\ 762242531345002495874*t+1) -(4142954896038016561375*t^2-972050475048958750994*t+19)/(t-1)/(t^2-\ 762242531345002495874*t+1) (3253270086169200779419*t^2-6424174507158258589850*t+31)/(t-1)/(t^2-\ 762242531345002495874*t+1) Then for all i>=0 we have 3 3 3 18 a(i) + 25 b(i) + 25 c(i) = -219006 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 387, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 3 (67673485085346825847 t + 2322371476352445014498 t - 9) ) a(i) t = ---------------------------------------------------------- / 2 ----- (t - 1) (t - 7093946910336019700834 t + 1) i = 0 infinity ----- 2 \ i 223660142366427901091 t + 1985791102976890883990 t + 23 ) b(i) t = - -------------------------------------------------------- / 2 ----- (t - 1) (t - 7093946910336019700834 t + 1) i = 0 infinity ----- 2 \ i 181655910244488491945 t - 2391107155587807277078 t + 29 ) c(i) t = -------------------------------------------------------- / 2 ----- (t - 1) (t - 7093946910336019700834 t + 1) i = 0 In Maple notation, these generating functions are 3*(67673485085346825847*t^2+2322371476352445014498*t-9)/(t-1)/(t^2-\ 7093946910336019700834*t+1) -(223660142366427901091*t^2+1985791102976890883990*t+23)/(t-1)/(t^2-\ 7093946910336019700834*t+1) (181655910244488491945*t^2-2391107155587807277078*t+29)/(t-1)/(t^2-\ 7093946910336019700834*t+1) Then for all i>=0 we have 3 3 3 18 a(i) + 29 b(i) + 29 c(i) = -144 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 388, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (29897422467103138886247072627811 t / ----- i = 0 / + 1104590025411987876511716196057018 t - 29) / ((t - 1) / 2 (t - 1123928619512067417529729898035202 t + 1)) infinity ----- \ i ) b(i) t = - 5 ( / ----- i = 0 2 6548803765308061323525489585509 t + 58915932110238245459521408442006 t + 5 / 2 ) / ((t - 1) (t - 1123928619512067417529729898035202 t + 1)) / infinity ----- \ i 2 ) c(i) t = (26957420929681634575128014515711 t / ----- i = 0 / - 354281100307413168490362504653342 t + 31) / ((t - 1) / 2 (t - 1123928619512067417529729898035202 t + 1)) In Maple notation, these generating functions are (29897422467103138886247072627811*t^2+1104590025411987876511716196057018*t-29)/ (t-1)/(t^2-1123928619512067417529729898035202*t+1) -5*(6548803765308061323525489585509*t^2+58915932110238245459521408442006*t+5)/( t-1)/(t^2-1123928619512067417529729898035202*t+1) (26957420929681634575128014515711*t^2-354281100307413168490362504653342*t+31)/( t-1)/(t^2-1123928619512067417529729898035202*t+1) Then for all i>=0 we have 3 3 3 18 a(i) + 31 b(i) + 31 c(i) = -144 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 389, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 30 ( / ----- i = 0 2 6731203043306455457777738097301 t + 27714103425574581591126002171904 t - 1 / 2 ) / ((t - 1) (t - 158207014078095113561541707328098 t + 1)) / infinity ----- \ i 2 ) b(i) t = - (215860768787286349522427254280681 t / ----- i = 0 / - 275858758332796887509505210376 t + 23) / ((t - 1) / 2 (t - 158207014078095113561541707328098 t + 1)) infinity ----- \ i 2 ) c(i) t = (187683639768794210396846025036167 t / ----- i = 0 / - 403268549797747763031763774106524 t + 29) / ((t - 1) / 2 (t - 158207014078095113561541707328098 t + 1)) In Maple notation, these generating functions are 30*(6731203043306455457777738097301*t^2+27714103425574581591126002171904*t-1)/( t-1)/(t^2-158207014078095113561541707328098*t+1) -(215860768787286349522427254280681*t^2-275858758332796887509505210376*t+23)/(t -1)/(t^2-158207014078095113561541707328098*t+1) (187683639768794210396846025036167*t^2-403268549797747763031763774106524*t+29)/ (t-1)/(t^2-158207014078095113561541707328098*t+1) Then for all i>=0 we have 3 3 3 18 a(i) + 43 b(i) + 43 c(i) = -39546 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 390, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 9 (119427023615569034313070534137535930589186199615391877\ / ----- i = 0 2 832878793243336891160972064797235960822557 t + 140575721255772791186116\ 227317554472259849310792438146236138902203745503513150802075439504577446 t / 2 - 3) / ((t - 1) (t - 18604447701339111175416077584182748382129784909\ / 6995180613715534385400860322345823244569065518402 t + 1)) infinity ----- \ i ) b(i) t = - 16 (530106490184993040939186952081564717778772987424612\ / ----- i = 0 2 19747429365701377290808013330789994396249231 t - 2780222367290968550012\ 049719442509898518343159908856446390515553794425092775220801486829350923\ / 2 2 t + 1) / ((t - 1) (t - 18604447701339111175416077584182748382129784\ / 9096995180613715534385400860322345823244569065518402 t + 1)) infinity ----- \ i ) c(i) t = 2 (362075006809141280319562938170761964109402478600928590\ / ----- i = 0 2 643132475273131863745909612675236498028291 t - 563742409573858229069948\ 522280612946450953415747909832911326156580596182787998594876245319948302 t / 2 + 11) / ((t - 1) (t - 1860444770133911117541607758418274838212978490\ / 96995180613715534385400860322345823244569065518402 t + 1)) In Maple notation, these generating functions are 9*(1194270236155690343130705341375359305891861996153918778328787932433368911609\ 72064797235960822557*t^2+140575721255772791186116227317554472259849310792438146\ 236138902203745503513150802075439504577446*t-3)/(t-1)/(t^2-18604447701339111175\ 4160775841827483821297849096995180613715534385400860322345823244569065518402*t+ 1) -16*(53010649018499304093918695208156471777877298742461219747429365701377290808\ 013330789994396249231*t^2-27802223672909685500120497194425098985183431599088564\ 463905155537944250927752208014868293509232*t+1)/(t-1)/(t^2-18604447701339111175\ 4160775841827483821297849096995180613715534385400860322345823244569065518402*t+ 1) 2*(3620750068091412803195629381707619641094024786009285906431324752731318637459\ 09612675236498028291*t^2-563742409573858229069948522280612946450953415747909832\ 911326156580596182787998594876245319948302*t+11)/(t-1)/(t^2-1860444770133911117\ 54160775841827483821297849096995180613715534385400860322345823244569065518402*t +1) Then for all i>=0 we have 3 3 3 18 a(i) + 97 b(i) + 97 c(i) = -281250 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 391, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 28 (2100229932602623315234399 t + 3352452563044840305186402 t - 1) ------------------------------------------------------------------- 2 (t - 1) (t - 13792262641935036624780802 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 79799190322746026490293347 t - 34188701522676047778597374 t + 27 - ----------------------------------------------------------------- 2 (t - 1) (t - 13792262641935036624780802 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 68037902700171335924980717 t - 113648391500241314636676754 t + 37 ------------------------------------------------------------------ 2 (t - 1) (t - 13792262641935036624780802 t + 1) In Maple notation, these generating functions are 28*(2100229932602623315234399*t^2+3352452563044840305186402*t-1)/(t-1)/(t^2-\ 13792262641935036624780802*t+1) -(79799190322746026490293347*t^2-34188701522676047778597374*t+27)/(t-1)/(t^2-\ 13792262641935036624780802*t+1) (68037902700171335924980717*t^2-113648391500241314636676754*t+37)/(t-1)/(t^2-\ 13792262641935036624780802*t+1) Then for all i>=0 we have 3 3 3 19 a(i) + 20 b(i) + 20 c(i) = -202312 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 392, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 3 (174233 t + 40992878 t - 7) ) a(i) t = ------------------------------ / 2 ----- (t - 1) (t - 146361602 t + 1) i = 0 infinity ----- 2 \ i 497905 t + 116033806 t + 1 ) b(i) t = - ------------------------------ / 2 ----- (t - 1) (t - 146361602 t + 1) i = 0 infinity ----- 2 \ i 4 (11621 t - 29144554 t + 5) ) c(i) t = ------------------------------ / 2 ----- (t - 1) (t - 146361602 t + 1) i = 0 In Maple notation, these generating functions are 3*(174233*t^2+40992878*t-7)/(t-1)/(t^2-146361602*t+1) -(497905*t^2+116033806*t+1)/(t-1)/(t^2-146361602*t+1) 4*(11621*t^2-29144554*t+5)/(t-1)/(t^2-146361602*t+1) Then for all i>=0 we have 3 3 3 19 a(i) + 22 b(i) + 22 c(i) = -19 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 393, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 24 (25328132723798270683922500091025014448772524694013999 t / ----- i = 0 / + 53765906822737219529340239793897060516087772057986002 t - 1) / ( / 2 (t - 1) (t - 187767963801531407660753821515424763331213062208000002 t + 1) ) infinity ----- \ i ) b(i) t = - 4 ( / ----- i = 0 2 146194029512713379481760415199439653335131335494394001 t / + 183685989083812689456481743832796317859773804617605998 t + 1) / ( / 2 (t - 1) (t - 187767963801531407660753821515424763331213062208000002 t + 1) ) infinity ----- \ i 2 ) c(i) t = 25 (11233541014610970788798866388218337598210201825976321 t / ----- i = 0 / - 64014343990055141818917611833376092989395024243896322 t + 1) / ( / 2 (t - 1) (t - 187767963801531407660753821515424763331213062208000002 t + 1) ) In Maple notation, these generating functions are 24*(25328132723798270683922500091025014448772524694013999*t^2+ 53765906822737219529340239793897060516087772057986002*t-1)/(t-1)/(t^2-\ 187767963801531407660753821515424763331213062208000002*t+1) -4*(146194029512713379481760415199439653335131335494394001*t^2+ 183685989083812689456481743832796317859773804617605998*t+1)/(t-1)/(t^2-\ 187767963801531407660753821515424763331213062208000002*t+1) 25*(11233541014610970788798866388218337598210201825976321*t^2-\ 64014343990055141818917611833376092989395024243896322*t+1)/(t-1)/(t^2-\ 187767963801531407660753821515424763331213062208000002*t+1) Then for all i>=0 we have 3 3 3 19 a(i) + 24 b(i) + 24 c(i) = -110808 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 394, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 56027891 t + 1148604138 t - 29 ) a(i) t = ------------------------------- / 2 ----- (t - 1) (t - 384238402 t + 1) i = 0 infinity ----- 2 \ i 5 (9342841 t + 165335558 t + 1) ) b(i) t = - -------------------------------- / 2 ----- (t - 1) (t - 384238402 t + 1) i = 0 infinity ----- 2 \ i 8 (1925563 t - 111099566 t + 3) ) c(i) t = -------------------------------- / 2 ----- (t - 1) (t - 384238402 t + 1) i = 0 In Maple notation, these generating functions are (56027891*t^2+1148604138*t-29)/(t-1)/(t^2-384238402*t+1) -5*(9342841*t^2+165335558*t+1)/(t-1)/(t^2-384238402*t+1) 8*(1925563*t^2-111099566*t+3)/(t-1)/(t^2-384238402*t+1) Then for all i>=0 we have 3 3 3 19 a(i) + 34 b(i) + 34 c(i) = -2375 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 395, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 28 (22333284293043980339 t + 285099726525988162574 t - 1) ) a(i) t = ---------------------------------------------------------- / 2 ----- (t - 1) (t - 1985682584286854353154 t + 1) i = 0 infinity ----- \ i ) b(i) t = / ----- i = 0 2 4 (129303687583164904237 t + 1398018260509251985042 t + 1) - ----------------------------------------------------------- 2 (t - 1) (t - 1985682584286854353154 t + 1) infinity ----- 2 \ i 23 (7728209959930048513 t - 273349418323828637954 t + 1) ) c(i) t = --------------------------------------------------------- / 2 ----- (t - 1) (t - 1985682584286854353154 t + 1) i = 0 In Maple notation, these generating functions are 28*(22333284293043980339*t^2+285099726525988162574*t-1)/(t-1)/(t^2-\ 1985682584286854353154*t+1) -4*(129303687583164904237*t^2+1398018260509251985042*t+1)/(t-1)/(t^2-\ 1985682584286854353154*t+1) 23*(7728209959930048513*t^2-273349418323828637954*t+1)/(t-1)/(t^2-\ 1985682584286854353154*t+1) Then for all i>=0 we have 3 3 3 19 a(i) + 35 b(i) + 35 c(i) = -6517 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 396, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 3 (956071 t + 6977378 t - 9) ) a(i) t = ----------------------------- / 2 ----- (t - 1) (t - 3928322 t + 1) i = 0 infinity ----- 2 \ i 3 (778961 t + 4620078 t + 1) ) b(i) t = - ----------------------------- / 2 ----- (t - 1) (t - 3928322 t + 1) i = 0 infinity ----- 2 \ i 2 (432011 t - 8530582 t + 11) ) c(i) t = ------------------------------ / 2 ----- (t - 1) (t - 3928322 t + 1) i = 0 In Maple notation, these generating functions are 3*(956071*t^2+6977378*t-9)/(t-1)/(t^2-3928322*t+1) -3*(778961*t^2+4620078*t+1)/(t-1)/(t^2-3928322*t+1) 2*(432011*t^2-8530582*t+11)/(t-1)/(t^2-3928322*t+1) Then for all i>=0 we have 3 3 3 19 a(i) + 37 b(i) + 37 c(i) = -19000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 397, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 26 (99812781243013776504092087026485978090362098680413399 t / ----- i = 0 / + 117136826565098643564638514366984686538803108550325802 t - 1) / ( / 2 (t - 1) (t - 469316067994993981268555236295181414099211485357979202 t + 1) ) infinity ----- \ i ) b(i) t = - ( / ----- i = 0 2 3394367050940391083511936631590186243173611685775718949 t / - 2549153279195852159900320566224456682236643133946182978 t + 29) / ( / 2 (t - 1) (t - 469316067994993981268555236295181414099211485357979202 t + 1) ) infinity ----- \ i ) c(i) t = 2 ( / ----- i = 0 2 1567426909854277632300648602660661350069335114603322057 t / - 1990033795726547094106456635343526130537819390518090074 t + 17) / ( / 2 (t - 1) (t - 469316067994993981268555236295181414099211485357979202 t + 1) ) In Maple notation, these generating functions are 26*(99812781243013776504092087026485978090362098680413399*t^2+ 117136826565098643564638514366984686538803108550325802*t-1)/(t-1)/(t^2-\ 469316067994993981268555236295181414099211485357979202*t+1) -(3394367050940391083511936631590186243173611685775718949*t^2-\ 2549153279195852159900320566224456682236643133946182978*t+29)/(t-1)/(t^2-\ 469316067994993981268555236295181414099211485357979202*t+1) 2*(1567426909854277632300648602660661350069335114603322057*t^2-\ 1990033795726547094106456635343526130537819390518090074*t+17)/(t-1)/(t^2-\ 469316067994993981268555236295181414099211485357979202*t+1) Then for all i>=0 we have 3 3 3 19 a(i) + 40 b(i) + 40 c(i) = -262656 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 398, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 3691393264150716969878011 t + 21495604332063440205590818 t - 29 ---------------------------------------------------------------- 2 (t - 1) (t - 3587269802684006672654402 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 4 (732137387181454683357841 t + 3220455507147882230358958 t + 1) - ----------------------------------------------------------------- 2 (t - 1) (t - 3587269802684006672654402 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 1217903889729145015683023 t - 17028275467046492670550246 t + 23 ---------------------------------------------------------------- 2 (t - 1) (t - 3587269802684006672654402 t + 1) In Maple notation, these generating functions are (3691393264150716969878011*t^2+21495604332063440205590818*t-29)/(t-1)/(t^2-\ 3587269802684006672654402*t+1) -4*(732137387181454683357841*t^2+3220455507147882230358958*t+1)/(t-1)/(t^2-\ 3587269802684006672654402*t+1) (1217903889729145015683023*t^2-17028275467046492670550246*t+23)/(t-1)/(t^2-\ 3587269802684006672654402*t+1) Then for all i>=0 we have 3 3 3 19 a(i) + 41 b(i) + 41 c(i) = -32832 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 399, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 21 (93595497203563198775815949852046099200265441924073205\ / ----- i = 0 2 32711997188540808007101999 t + 9370863583942721835283352796855620663400\ / 2 111832339808584491200190234950723898002 t - 1) / ((t - 1) (t - 374382\ / 023004865961924168121484663822411720826971626619168577665497392799330000\ 02 t + 1)) infinity ----- \ i ) b(i) t = - (292572223041323850802840292184798578947180491964656008\ / ----- i = 0 2 910390890721085453710021029 t - 250445761337734622373878972236903619328\ / 2 731437923223665634845167774699174712021058 t + 29) / ((t - 1) (t - 37\ / 438202300486596192416812148466382241172082697162661916857766549739279933\ 000002 t + 1)) infinity ----- \ i ) c(i) t = 32 (87041530768996678433271218658434895020981461148764071\ / ----- i = 0 2 28478840466821070053105251 t - 1002060500513683123173216311421520699017\ / 2 4679053671167855839644308895641271792752 t + 1) / ((t - 1) (t - 37438\ / 202300486596192416812148466382241172082697162661916857766549739279933000\ 002 t + 1)) In Maple notation, these generating functions are 21*(935954972035631987758159498520460992002654419240732053271199718854080800710\ 1999*t^2+9370863583942721835283352796855620663400111832339808584491200190234950\ 723898002*t-1)/(t-1)/(t^2-37438202300486596192416812148466382241172082697162661\ 916857766549739279933000002*t+1) -(29257222304132385080284029218479857894718049196465600891039089072108545371002\ 1029*t^2-2504457613377346223738789722369036193287314379232236656348451677746991\ 74712021058*t+29)/(t-1)/(t^2-37438202300486596192416812148466382241172082697162\ 661916857766549739279933000002*t+1) 32*(870415307689966784332712186584348950209814611487640712847884046682107005310\ 5251*t^2-1002060500513683123173216311421520699017467905367116785583964430889564\ 1271792752*t+1)/(t-1)/(t^2-3743820230048659619241681214846638224117208269716266\ 1916857766549739279933000002*t+1) Then for all i>=0 we have 3 3 3 19 a(i) + 42 b(i) + 42 c(i) = -175959 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 400, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (108029573080567700678559148879246520974414031981 t / ----- i = 0 / + 285366122674364627419643143282669028096494652006 t - 19) / ((t - 1) / 2 (t - 71488857820457234712912689743017018403593909314 t + 1)) infinity ----- \ i 2 ) b(i) t = - (160550547109538303311340537464391660364388357175 t / ----- i = 0 / - 121224776050206239646665808153221568647373634318 t + 23) / ((t - 1) / 2 (t - 71488857820457234712912689743017018403593909314 t + 1)) infinity ----- \ i 2 ) c(i) t = (153348575570833789932769927539108558966094088377 t / ----- i = 0 / - 192674346630165853597444656850278650683108811282 t + 25) / ((t - 1) / 2 (t - 71488857820457234712912689743017018403593909314 t + 1)) In Maple notation, these generating functions are (108029573080567700678559148879246520974414031981*t^2+ 285366122674364627419643143282669028096494652006*t-19)/(t-1)/(t^2-\ 71488857820457234712912689743017018403593909314*t+1) -(160550547109538303311340537464391660364388357175*t^2-\ 121224776050206239646665808153221568647373634318*t+23)/(t-1)/(t^2-\ 71488857820457234712912689743017018403593909314*t+1) (153348575570833789932769927539108558966094088377*t^2-\ 192674346630165853597444656850278650683108811282*t+25)/(t-1)/(t^2-\ 71488857820457234712912689743017018403593909314*t+1) Then for all i>=0 we have 3 3 3 19 a(i) + 45 b(i) + 45 c(i) = -25289 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 401, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (246566161137014837800496084234376033955 t / ----- i = 0 / + 801497204602143707010530902810201535866 t - 29) / ((t - 1) / 2 (t - 108764711678697784206192949322142544898 t + 1)) infinity ----- \ i 2 ) b(i) t = - 4 (47551855927847131884802375992094674625 t / ----- i = 0 / + 102024790325586011185876524510348303166 t + 1) / ((t - 1) / 2 (t - 108764711678697784206192949322142544898 t + 1)) infinity ----- \ i 2 ) c(i) t = 23 (3841951256257646832319670682506876641 t / ----- i = 0 / - 29855281039463410844611653378583916258 t + 1) / ((t - 1) / 2 (t - 108764711678697784206192949322142544898 t + 1)) In Maple notation, these generating functions are (246566161137014837800496084234376033955*t^2+ 801497204602143707010530902810201535866*t-29)/(t-1)/(t^2-\ 108764711678697784206192949322142544898*t+1) -4*(47551855927847131884802375992094674625*t^2+ 102024790325586011185876524510348303166*t+1)/(t-1)/(t^2-\ 108764711678697784206192949322142544898*t+1) 23*(3841951256257646832319670682506876641*t^2-\ 29855281039463410844611653378583916258*t+1)/(t-1)/(t^2-\ 108764711678697784206192949322142544898*t+1) Then for all i>=0 we have 3 3 3 19 a(i) + 46 b(i) + 46 c(i) = -93347 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 402, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (928906912190097603565139091427815073543 t / ----- i = 0 / + 1493922131644101730819163346371944608018 t - 25) / ((t - 1) / 2 (t - 195300235371557756081597169057362355202 t + 1)) infinity ----- \ i 2 ) b(i) t = - (712992669646819659312950832872035529635 t / ----- i = 0 / + 645190843312339164042467922278739985498 t + 3) / ((t - 1) / 2 (t - 195300235371557756081597169057362355202 t + 1)) infinity ----- \ i 2 ) c(i) t = 22 (15339868609079951179855944301602691969 t / ----- i = 0 / - 77075482834496261332374978626637942658 t + 1) / ((t - 1) / 2 (t - 195300235371557756081597169057362355202 t + 1)) In Maple notation, these generating functions are (928906912190097603565139091427815073543*t^2+ 1493922131644101730819163346371944608018*t-25)/(t-1)/(t^2-\ 195300235371557756081597169057362355202*t+1) -(712992669646819659312950832872035529635*t^2+ 645190843312339164042467922278739985498*t+3)/(t-1)/(t^2-\ 195300235371557756081597169057362355202*t+1) 22*(15339868609079951179855944301602691969*t^2-\ 77075482834496261332374978626637942658*t+1)/(t-1)/(t^2-\ 195300235371557756081597169057362355202*t+1) Then for all i>=0 we have 3 3 3 19 a(i) + 47 b(i) + 47 c(i) = -202312 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 403, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 4 (396060305592130659996227707 t + 687792374405414911341701002 t - 5) ---------------------------------------------------------------------- 2 (t - 1) (t - 505596082568687459255402498 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 1249043472498320990426871941 t + 821781201016542615146153846 t + 5 - ------------------------------------------------------------------- 2 (t - 1) (t - 505596082568687459255402498 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 720963065042146777098568337 t - 2791787738557010382671594146 t + 17 -------------------------------------------------------------------- 2 (t - 1) (t - 505596082568687459255402498 t + 1) In Maple notation, these generating functions are 4*(396060305592130659996227707*t^2+687792374405414911341701002*t-5)/(t-1)/(t^2-\ 505596082568687459255402498*t+1) -(1249043472498320990426871941*t^2+821781201016542615146153846*t+5)/(t-1)/(t^2-\ 505596082568687459255402498*t+1) (720963065042146777098568337*t^2-2791787738557010382671594146*t+17)/(t-1)/(t^2-\ 505596082568687459255402498*t+1) Then for all i>=0 we have 3 3 3 19 a(i) + 48 b(i) + 48 c(i) = -77824 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 404, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 28 (36467717 t + 76622636 t - 1) ) a(i) t = --------------------------------- / 2 ----- (t - 1) (t - 269944898 t + 1) i = 0 infinity ----- 2 \ i 4 (194077951 t + 234167152 t + 1) ) b(i) t = - ---------------------------------- / 2 ----- (t - 1) (t - 269944898 t + 1) i = 0 infinity ----- 2 \ i 380376599 t - 2093357038 t + 23 ) c(i) t = -------------------------------- / 2 ----- (t - 1) (t - 269944898 t + 1) i = 0 In Maple notation, these generating functions are 28*(36467717*t^2+76622636*t-1)/(t-1)/(t^2-269944898*t+1) -4*(194077951*t^2+234167152*t+1)/(t-1)/(t^2-269944898*t+1) (380376599*t^2-2093357038*t+23)/(t-1)/(t^2-269944898*t+1) Then for all i>=0 we have 3 3 3 19 a(i) + 49 b(i) + 49 c(i) = -175959 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 405, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 9 (24697997 t + 41063606 t - 3) ) a(i) t = -------------------------------- / 2 ----- (t - 1) (t - 46267202 t + 1) i = 0 infinity ----- 2 \ i 4 (42057601 t + 36602398 t + 1) ) b(i) t = - -------------------------------- / 2 ----- (t - 1) (t - 46267202 t + 1) i = 0 infinity ----- 2 \ i 23 (3641881 t - 17321882 t + 1) ) c(i) t = -------------------------------- / 2 ----- (t - 1) (t - 46267202 t + 1) i = 0 In Maple notation, these generating functions are 9*(24697997*t^2+41063606*t-3)/(t-1)/(t^2-46267202*t+1) -4*(42057601*t^2+36602398*t+1)/(t-1)/(t^2-46267202*t+1) 23*(3641881*t^2-17321882*t+1)/(t-1)/(t^2-46267202*t+1) Then for all i>=0 we have 3 3 3 19 a(i) + 50 b(i) + 50 c(i) = -231173 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 406, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 20232300999393811136950565779 t + 34680792999382694513367424138 t - 29 ----------------------------------------------------------------------- 2 (t - 1) (t - 4161648389060980786552992002 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 15118486312664667001334240981 t + 12627367002321756074365817126 t + 5 - ---------------------------------------------------------------------- 2 (t - 1) (t - 4161648389060980786552992002 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 24 (327724886464422122223784609 t - 1483802107922189750377953698 t + 1) ------------------------------------------------------------------------ 2 (t - 1) (t - 4161648389060980786552992002 t + 1) In Maple notation, these generating functions are (20232300999393811136950565779*t^2+34680792999382694513367424138*t-29)/(t-1)/(t ^2-4161648389060980786552992002*t+1) -(15118486312664667001334240981*t^2+12627367002321756074365817126*t+5)/(t-1)/(t ^2-4161648389060980786552992002*t+1) 24*(327724886464422122223784609*t^2-1483802107922189750377953698*t+1)/(t-1)/(t^ 2-4161648389060980786552992002*t+1) Then for all i>=0 we have 3 3 3 19 a(i) + 53 b(i) + 53 c(i) = -262656 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 407, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 22 (2735305524599649933135026029544130124799 t / ----- i = 0 / + 7933504719542831345597558022864100553474 t - 1) / ((t - 1) / 2 (t - 39097606083121818339866542322042177963522 t + 1)) infinity ----- \ i 2 ) b(i) t = - (77483722359041164226991537178564068335975 t / ----- i = 0 / - 56781219465847152220799909030990915086462 t + 23) / ((t - 1) / 2 (t - 39097606083121818339866542322042177963522 t + 1)) infinity ----- \ i 2 ) c(i) t = (73943915209559264313522679963859899939177 t / ----- i = 0 / - 94646418102753276319714308111433053188738 t + 25) / ((t - 1) / 2 (t - 39097606083121818339866542322042177963522 t + 1)) In Maple notation, these generating functions are 22*(2735305524599649933135026029544130124799*t^2+ 7933504719542831345597558022864100553474*t-1)/(t-1)/(t^2-\ 39097606083121818339866542322042177963522*t+1) -(77483722359041164226991537178564068335975*t^2-\ 56781219465847152220799909030990915086462*t+23)/(t-1)/(t^2-\ 39097606083121818339866542322042177963522*t+1) (73943915209559264313522679963859899939177*t^2-\ 94646418102753276319714308111433053188738*t+25)/(t-1)/(t^2-\ 39097606083121818339866542322042177963522*t+1) Then for all i>=0 we have 3 3 3 19 a(i) + 68 b(i) + 68 c(i) = -32832 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 408, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 26 (7436686344692729493599 t + 154537976793036266492834 t - 1) --------------------------------------------------------------- 2 (t - 1) (t - 1772570183603282854382594 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 127877356632532806307013 t + 2132447038566284256328502 t + 5 - ------------------------------------------------------------- 2 (t - 1) (t - 1772570183603282854382594 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 50535818647728419573585 t - 2310860213846545482209122 t + 17 ------------------------------------------------------------- 2 (t - 1) (t - 1772570183603282854382594 t + 1) In Maple notation, these generating functions are 26*(7436686344692729493599*t^2+154537976793036266492834*t-1)/(t-1)/(t^2-\ 1772570183603282854382594*t+1) -(127877356632532806307013*t^2+2132447038566284256328502*t+5)/(t-1)/(t^2-\ 1772570183603282854382594*t+1) (50535818647728419573585*t^2-2310860213846545482209122*t+17)/(t-1)/(t^2-\ 1772570183603282854382594*t+1) Then for all i>=0 we have 3 3 3 19 a(i) + 70 b(i) + 70 c(i) = -1216 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 409, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 2 / ----- i = 0 2 (30310349724801048151480956469 t + 41521625624864230027144067542 t - 11) / 2 / ((t - 1) (t - 13430143872068638095395942402 t + 1)) / infinity ----- \ i ) b(i) t = / ----- i = 0 2 5 (8291917251227144497947206401 t + 3487134981364378881057619198 t + 1) - ------------------------------------------------------------------------ 2 (t - 1) (t - 13430143872068638095395942402 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 24139386413392266403175485457 t - 83034647576349883298199613474 t + 17 ----------------------------------------------------------------------- 2 (t - 1) (t - 13430143872068638095395942402 t + 1) In Maple notation, these generating functions are 2*(30310349724801048151480956469*t^2+41521625624864230027144067542*t-11)/(t-1)/ (t^2-13430143872068638095395942402*t+1) -5*(8291917251227144497947206401*t^2+3487134981364378881057619198*t+1)/(t-1)/(t ^2-13430143872068638095395942402*t+1) (24139386413392266403175485457*t^2-83034647576349883298199613474*t+17)/(t-1)/(t ^2-13430143872068638095395942402*t+1) Then for all i>=0 we have 3 3 3 19 a(i) + 74 b(i) + 74 c(i) = -152000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 410, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 18 (28964131999 t + 629673148002 t - 1) ) a(i) t = ---------------------------------------- / 2 ----- (t - 1) (t - 11850792480002 t + 1) i = 0 infinity ----- 2 \ i 3 (223004634007 t + 73304165986 t + 7) ) b(i) t = - --------------------------------------- / 2 ----- (t - 1) (t - 11850792480002 t + 1) i = 0 infinity ----- 2 \ i 2 (321473091611 t - 765936291622 t + 11) ) c(i) t = ----------------------------------------- / 2 ----- (t - 1) (t - 11850792480002 t + 1) i = 0 In Maple notation, these generating functions are 18*(28964131999*t^2+629673148002*t-1)/(t-1)/(t^2-11850792480002*t+1) -3*(223004634007*t^2+73304165986*t+7)/(t-1)/(t^2-11850792480002*t+1) 2*(321473091611*t^2-765936291622*t+11)/(t-1)/(t^2-11850792480002*t+1) Then for all i>=0 we have 3 3 3 19 a(i) + 80 b(i) + 80 c(i) = -152 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 411, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 10 ( / ----- i = 0 2 293804871142819687012510182683174973543938497404283731055561227367243583 t + 561396986928993095980493588395216478448698693043140233849171085586522818 t / 2 - 1) / ((t - 1) (t - / 1895312225996990492038548898065624299010709449099696354653731071951590402 t + 1)) infinity ----- \ i ) b(i) t = - ( / ----- i = 0 1858096692275440755481035165553232491270320480985044386274883811937409441 2 t + 2094322705840234538892036316998252327398354101893590694771311472254321758 t / 2 + 1) / ((t - 1) (t - / 1895312225996990492038548898065624299010709449099696354653731071951590402 t + 1)) infinity ----- \ i ) c(i) t = 7 ( / ----- i = 0 2 125535303114196447443714460467997511351027450900585516584239960101894881 t - 690166645702150060925581815118209628303695248454676242447982143557856482 t / 2 + 1) / ((t - 1) (t - / 1895312225996990492038548898065624299010709449099696354653731071951590402 t + 1)) In Maple notation, these generating functions are 10*(293804871142819687012510182683174973543938497404283731055561227367243583*t^ 2+561396986928993095980493588395216478448698693043140233849171085586522818*t-1) /(t-1)/(t^2-\ 1895312225996990492038548898065624299010709449099696354653731071951590402*t+1) -(1858096692275440755481035165553232491270320480985044386274883811937409441*t^2 +2094322705840234538892036316998252327398354101893590694771311472254321758*t+1) /(t-1)/(t^2-\ 1895312225996990492038548898065624299010709449099696354653731071951590402*t+1) 7*(125535303114196447443714460467997511351027450900585516584239960101894881*t^2 -690166645702150060925581815118209628303695248454676242447982143557856482*t+1)/ (t-1)/(t^2-\ 1895312225996990492038548898065624299010709449099696354653731071951590402*t+1) Then for all i>=0 we have 3 3 3 19 a(i) + 84 b(i) + 84 c(i) = -9728 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 412, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (82617142777025339522434570229095553394669955672895393167 t / ----- i = 0 / + 251393163853032166154809683572449962376570103930823399106 t - 17) / ( / (t - 1) 2 (t - 74103287295588534598067515010982177735528398146124991554 t + 1)) infinity ----- \ i ) b(i) t = - 13 ( / ----- i = 0 2 6287749459144287329627596600753933119516399933513426385 t / - 3326388831066315977379514089214332186406945368664776338 t + 1) / ( / (t - 1) 2 (t - 74103287295588534598067515010982177735528398146124991554 t + 1)) infinity ----- \ i ) c(i) t = 3 ( / ----- i = 0 2 25128526046624595363708442443546644712912862386945478613 t / - 37961088768295804556783466660218248756387165501289628826 t + 5) / ( / (t - 1) 2 (t - 74103287295588534598067515010982177735528398146124991554 t + 1)) In Maple notation, these generating functions are (82617142777025339522434570229095553394669955672895393167*t^2+ 251393163853032166154809683572449962376570103930823399106*t-17)/(t-1)/(t^2-\ 74103287295588534598067515010982177735528398146124991554*t+1) -13*(6287749459144287329627596600753933119516399933513426385*t^2-\ 3326388831066315977379514089214332186406945368664776338*t+1)/(t-1)/(t^2-\ 74103287295588534598067515010982177735528398146124991554*t+1) 3*(25128526046624595363708442443546644712912862386945478613*t^2-\ 37961088768295804556783466660218248756387165501289628826*t+5)/(t-1)/(t^2-\ 74103287295588534598067515010982177735528398146124991554*t+1) Then for all i>=0 we have 3 3 3 19 a(i) + 91 b(i) + 91 c(i) = -13851 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 413, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 18 ( / ----- i = 0 2 9623331652084997662513123862111 t + 57121247983229836748289267381218 t - 1 / 2 ) / ((t - 1) (t - 397518044669248252734713423460674 t + 1)) / infinity ----- \ i 2 ) b(i) t = - 2 (68256155391657118780159612193477 t / ----- i = 0 / + 43822304028691522963675499779766 t + 5) / ((t - 1) / 2 (t - 397518044669248252734713423460674 t + 1)) infinity ----- \ i 2 ) c(i) t = (114859814566122992819664695697205 t / ----- i = 0 / - 339016733406820276307334919643714 t + 13) / ((t - 1) / 2 (t - 397518044669248252734713423460674 t + 1)) In Maple notation, these generating functions are 18*(9623331652084997662513123862111*t^2+57121247983229836748289267381218*t-1)/( t-1)/(t^2-397518044669248252734713423460674*t+1) -2*(68256155391657118780159612193477*t^2+43822304028691522963675499779766*t+5)/ (t-1)/(t^2-397518044669248252734713423460674*t+1) (114859814566122992819664695697205*t^2-339016733406820276307334919643714*t+13)/ (t-1)/(t^2-397518044669248252734713423460674*t+1) Then for all i>=0 we have 3 3 3 19 a(i) + 96 b(i) + 96 c(i) = -4104 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 414, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 1166169963450654937331 t + 3064667375599219371498 t - 29 ) a(i) t = --------------------------------------------------------- / 2 ----- (t - 1) (t - 493360918407631572802 t + 1) i = 0 infinity ----- 2 \ i 8 (183918066953198029283 t - 12478217062170705286 t + 3) ) b(i) t = - --------------------------------------------------------- / 2 ----- (t - 1) (t - 493360918407631572802 t + 1) i = 0 infinity ----- 2 \ i 34 (35818509593523225961 t - 76157297803176713962 t + 1) ) c(i) t = --------------------------------------------------------- / 2 ----- (t - 1) (t - 493360918407631572802 t + 1) i = 0 In Maple notation, these generating functions are (1166169963450654937331*t^2+3064667375599219371498*t-29)/(t-1)/(t^2-\ 493360918407631572802*t+1) -8*(183918066953198029283*t^2-12478217062170705286*t+3)/(t-1)/(t^2-\ 493360918407631572802*t+1) 34*(35818509593523225961*t^2-76157297803176713962*t+1)/(t-1)/(t^2-\ 493360918407631572802*t+1) Then for all i>=0 we have 3 3 3 20 a(i) + 23 b(i) + 23 c(i) = -98260 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 415, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 27 (133844031606834671884553182605710106239 t / ----- i = 0 / + 245688469472189134894274866091093664962 t - 1) / ((t - 1) / 2 (t - 907788432349428849893174510729705428802 t + 1)) infinity ----- \ i 2 ) b(i) t = - 8 (437575013313818489718207482890315683361 t / ----- i = 0 / + 325730575448464026708485799404932124638 t + 1) / ((t - 1) / 2 (t - 907788432349428849893174510729705428802 t + 1)) infinity ----- \ i 2 ) c(i) t = 28 (71244812533344923537301305671724527561 t / ----- i = 0 / - 289332123608282785373499386327509615562 t + 1) / ((t - 1) / 2 (t - 907788432349428849893174510729705428802 t + 1)) In Maple notation, these generating functions are 27*(133844031606834671884553182605710106239*t^2+ 245688469472189134894274866091093664962*t-1)/(t-1)/(t^2-\ 907788432349428849893174510729705428802*t+1) -8*(437575013313818489718207482890315683361*t^2+ 325730575448464026708485799404932124638*t+1)/(t-1)/(t^2-\ 907788432349428849893174510729705428802*t+1) 28*(71244812533344923537301305671724527561*t^2-\ 289332123608282785373499386327509615562*t+1)/(t-1)/(t^2-\ 907788432349428849893174510729705428802*t+1) Then for all i>=0 we have 3 3 3 20 a(i) + 27 b(i) + 27 c(i) = -185220 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 416, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (20157427477050434123 t + 872011226667739126274 t - 13) ) a(i) t = ---------------------------------------------------------- / 2 ----- (t - 1) (t - 846746042550482310914 t + 1) i = 0 infinity ----- 2 \ i 3 (11916623326254828553 t + 485161012988805637366 t + 1) ) b(i) t = - --------------------------------------------------------- / 2 ----- (t - 1) (t - 846746042550482310914 t + 1) i = 0 infinity ----- 2 \ i 7946521734556990319 t - 1499179430679738388102 t + 23 ) c(i) t = ------------------------------------------------------ / 2 ----- (t - 1) (t - 846746042550482310914 t + 1) i = 0 In Maple notation, these generating functions are 2*(20157427477050434123*t^2+872011226667739126274*t-13)/(t-1)/(t^2-\ 846746042550482310914*t+1) -3*(11916623326254828553*t^2+485161012988805637366*t+1)/(t-1)/(t^2-\ 846746042550482310914*t+1) (7946521734556990319*t^2-1499179430679738388102*t+23)/(t-1)/(t^2-\ 846746042550482310914*t+1) Then for all i>=0 we have 3 3 3 20 a(i) + 29 b(i) + 29 c(i) = -540 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 417, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 6739800545588442244432550437 t + 1600023732194222336230868470966 t - 27 ------------------------------------------------------------------------ 2 (t - 1) (t - 1998272553799879144775905849154 t + 1) infinity ----- \ i ) b(i) t = - 2 / ----- i = 0 2 (2746844347035741236522240713 t + 641009599677908887915478986166 t + 1) / 2 / ((t - 1) (t - 1998272553799879144775905849154 t + 1)) / infinity ----- \ i ) c(i) t = 2 / ----- i = 0 2 (339772723611297577796329843 t - 644096216748555926729797556734 t + 11) / 2 / ((t - 1) (t - 1998272553799879144775905849154 t + 1)) / In Maple notation, these generating functions are (6739800545588442244432550437*t^2+1600023732194222336230868470966*t-27)/(t-1)/( t^2-1998272553799879144775905849154*t+1) -2*(2746844347035741236522240713*t^2+641009599677908887915478986166*t+1)/(t-1)/ (t^2-1998272553799879144775905849154*t+1) 2*(339772723611297577796329843*t^2-644096216748555926729797556734*t+11)/(t-1)/( t^2-1998272553799879144775905849154*t+1) Then for all i>=0 we have 3 3 3 20 a(i) + 37 b(i) + 37 c(i) = -20 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 418, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (702804517833361 t + 1045348742190058 t - 11) ) a(i) t = ------------------------------------------------ / 2 ----- (t - 1) (t - 284228780755394 t + 1) i = 0 infinity ----- 2 \ i 1116164484563893 t + 1085024100531466 t + 1 ) b(i) t = - -------------------------------------------- / 2 ----- (t - 1) (t - 284228780755394 t + 1) i = 0 infinity ----- 2 \ i 21 (22018706669893 t - 126837210722054 t + 1) ) c(i) t = ---------------------------------------------- / 2 ----- (t - 1) (t - 284228780755394 t + 1) i = 0 In Maple notation, these generating functions are 2*(702804517833361*t^2+1045348742190058*t-11)/(t-1)/(t^2-284228780755394*t+1) -(1116164484563893*t^2+1085024100531466*t+1)/(t-1)/(t^2-284228780755394*t+1) 21*(22018706669893*t^2-126837210722054*t+1)/(t-1)/(t^2-284228780755394*t+1) Then for all i>=0 we have 3 3 3 20 a(i) + 43 b(i) + 43 c(i) = -185220 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 419, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (37962086646508047563 t + 60733550125290141314 t - 13) ) a(i) t = --------------------------------------------------------- / 2 ----- (t - 1) (t - 15184705562202339074 t + 1) i = 0 infinity ----- 2 \ i 3 (19469005840668103273 t + 17717354803838711446 t + 1) ) b(i) t = - -------------------------------------------------------- / 2 ----- (t - 1) (t - 15184705562202339074 t + 1) i = 0 infinity ----- 2 \ i 23 (1192067784132998473 t - 6042462650807800394 t + 1) ) c(i) t = ------------------------------------------------------- / 2 ----- (t - 1) (t - 15184705562202339074 t + 1) i = 0 In Maple notation, these generating functions are 2*(37962086646508047563*t^2+60733550125290141314*t-13)/(t-1)/(t^2-\ 15184705562202339074*t+1) -3*(19469005840668103273*t^2+17717354803838711446*t+1)/(t-1)/(t^2-\ 15184705562202339074*t+1) 23*(1192067784132998473*t^2-6042462650807800394*t+1)/(t-1)/(t^2-\ 15184705562202339074*t+1) Then for all i>=0 we have 3 3 3 20 a(i) + 49 b(i) + 49 c(i) = -243340 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 420, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (313291739599099760457797350744000226644161681859 t / ----- i = 0 / + 420632908876281735805918565839471841211503284570 t - 29) / ((t - 1) / 2 (t - 58462285254240325123350208734488225655787812098 t + 1)) infinity ----- \ i 2 ) b(i) t = - 30 (14133636581755745814817375676075531392635709969 t / ----- i = 0 / - 8035076082224107969407733634559759978051375890 t + 1) / ((t - 1) / 2 (t - 58462285254240325123350208734488225655787812098 t + 1)) infinity ----- \ i 2 ) c(i) t = 3 (123931269173163027011629459497199745779459228477 t / ----- i = 0 / - 184916874168479405465725879912357459925302569290 t + 13) / ((t - 1) / 2 (t - 58462285254240325123350208734488225655787812098 t + 1)) In Maple notation, these generating functions are (313291739599099760457797350744000226644161681859*t^2+ 420632908876281735805918565839471841211503284570*t-29)/(t-1)/(t^2-\ 58462285254240325123350208734488225655787812098*t+1) -30*(14133636581755745814817375676075531392635709969*t^2-\ 8035076082224107969407733634559759978051375890*t+1)/(t-1)/(t^2-\ 58462285254240325123350208734488225655787812098*t+1) 3*(123931269173163027011629459497199745779459228477*t^2-\ 184916874168479405465725879912357459925302569290*t+13)/(t-1)/(t^2-\ 58462285254240325123350208734488225655787812098*t+1) Then for all i>=0 we have 3 3 3 21 a(i) + 26 b(i) + 26 c(i) = -328125 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 421, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 3966242840567650030782965731 t + 8830346210938180350497553466 t - 29 --------------------------------------------------------------------- 2 (t - 1) (t - 1323972986978545970615055362 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 18 (236352341545010790389463265 t + 27203740427893402825582366 t + 1) - ---------------------------------------------------------------------- 2 (t - 1) (t - 1323972986978545970615055362 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 6 (543796906278046953219099557 t - 1334465152196759532864236458 t + 5) ----------------------------------------------------------------------- 2 (t - 1) (t - 1323972986978545970615055362 t + 1) In Maple notation, these generating functions are (3966242840567650030782965731*t^2+8830346210938180350497553466*t-29)/(t-1)/(t^2 -1323972986978545970615055362*t+1) -18*(236352341545010790389463265*t^2+27203740427893402825582366*t+1)/(t-1)/(t^2 -1323972986978545970615055362*t+1) 6*(543796906278046953219099557*t^2-1334465152196759532864236458*t+5)/(t-1)/(t^2 -1323972986978545970615055362*t+1) Then for all i>=0 we have 3 3 3 21 a(i) + 31 b(i) + 31 c(i) = -144039 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 422, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 4 (42586959090754622623537941544925519693 t / ----- i = 0 / + 1593182485421592222176551918499363181914 t - 7) / ((t - 1) / 2 (t - 6297028892245301781375276285741523636802 t + 1)) infinity ----- \ i 2 ) b(i) t = - 8 (19352298432417585085086765249727835537 t / ----- i = 0 / + 339468993365207245076492834968900953461 t + 2) / ((t - 1) / 2 (t - 6297028892245301781375276285741523636802 t + 1)) infinity ----- \ i 2 ) c(i) t = 5 (20742807310087026706489718428782412133 t / ----- i = 0 / - 594856874186286754965017078778588474538 t + 5) / ((t - 1) / 2 (t - 6297028892245301781375276285741523636802 t + 1)) In Maple notation, these generating functions are 4*(42586959090754622623537941544925519693*t^2+ 1593182485421592222176551918499363181914*t-7)/(t-1)/(t^2-\ 6297028892245301781375276285741523636802*t+1) -8*(19352298432417585085086765249727835537*t^2+ 339468993365207245076492834968900953461*t+2)/(t-1)/(t^2-\ 6297028892245301781375276285741523636802*t+1) 5*(20742807310087026706489718428782412133*t^2-\ 594856874186286754965017078778588474538*t+5)/(t-1)/(t^2-\ 6297028892245301781375276285741523636802*t+1) Then for all i>=0 we have 3 3 3 21 a(i) + 40 b(i) + 40 c(i) = -168 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 423, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 102310055814599504747 t + 303755562178001852066 t - 13 ) a(i) t = ------------------------------------------------------- / 2 ----- (t - 1) (t - 90159635792970868802 t + 1) i = 0 infinity ----- 2 \ i 2 (41847689408640442441 t + 78939028913113304758 t + 1) ) b(i) t = - -------------------------------------------------------- / 2 ----- (t - 1) (t - 90159635792970868802 t + 1) i = 0 infinity ----- 2 \ i 39848212039595382851 t - 281421648683102877262 t + 11 ) c(i) t = ------------------------------------------------------ / 2 ----- (t - 1) (t - 90159635792970868802 t + 1) i = 0 In Maple notation, these generating functions are (102310055814599504747*t^2+303755562178001852066*t-13)/(t-1)/(t^2-\ 90159635792970868802*t+1) -2*(41847689408640442441*t^2+78939028913113304758*t+1)/(t-1)/(t^2-\ 90159635792970868802*t+1) (39848212039595382851*t^2-281421648683102877262*t+11)/(t-1)/(t^2-\ 90159635792970868802*t+1) Then for all i>=0 we have 3 3 3 21 a(i) + 43 b(i) + 43 c(i) = -10752 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 424, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 4 (319 t + 97369 t - 6) ) a(i) t = --------------------------- / 2 ----- (t - 1) (t - 454274 t + 1) i = 0 infinity ----- 2 \ i 1223 t + 370576 t + 1 ) b(i) t = - --------------------------- / 2 ----- (t - 1) (t - 454274 t + 1) i = 0 infinity ----- 2 \ i 101 t - 371924 t + 23 ) c(i) t = --------------------------- / 2 ----- (t - 1) (t - 454274 t + 1) i = 0 In Maple notation, these generating functions are 4*(319*t^2+97369*t-6)/(t-1)/(t^2-454274*t+1) -(1223*t^2+370576*t+1)/(t-1)/(t^2-454274*t+1) (101*t^2-371924*t+23)/(t-1)/(t^2-454274*t+1) Then for all i>=0 we have 3 3 3 22 a(i) + 25 b(i) + 25 c(i) = -22 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 425, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 5 (400638123316917009211 t + 2351268425337105447370 t - 5) ) a(i) t = ----------------------------------------------------------- / 2 ----- (t - 1) (t - 2040753956477625328898 t + 1) i = 0 infinity ----- \ i ) b(i) t = / ----- i = 0 2 2 (949970687350399444753 t + 4581780547507432498414 t + 1) - ----------------------------------------------------------- 2 (t - 1) (t - 2040753956477625328898 t + 1) infinity ----- 2 \ i 24 (28157055468018390057 t - 489136325039504385322 t + 1) ) c(i) t = ---------------------------------------------------------- / 2 ----- (t - 1) (t - 2040753956477625328898 t + 1) i = 0 In Maple notation, these generating functions are 5*(400638123316917009211*t^2+2351268425337105447370*t-5)/(t-1)/(t^2-\ 2040753956477625328898*t+1) -2*(949970687350399444753*t^2+4581780547507432498414*t+1)/(t-1)/(t^2-\ 2040753956477625328898*t+1) 24*(28157055468018390057*t^2-489136325039504385322*t+1)/(t-1)/(t^2-\ 2040753956477625328898*t+1) Then for all i>=0 we have 3 3 3 22 a(i) + 27 b(i) + 27 c(i) = -29282 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 426, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 4 (672161678 t + 33433429679 t - 7) ) a(i) t = ------------------------------------ / 2 ----- (t - 1) (t - 63505008002 t + 1) i = 0 infinity ----- 2 \ i 3 (801771811 t + 37868241988 t + 1) ) b(i) t = - ------------------------------------ / 2 ----- (t - 1) (t - 63505008002 t + 1) i = 0 infinity ----- 2 \ i 25 (19889743 t - 4660291400 t + 1) ) c(i) t = ----------------------------------- / 2 ----- (t - 1) (t - 63505008002 t + 1) i = 0 In Maple notation, these generating functions are 4*(672161678*t^2+33433429679*t-7)/(t-1)/(t^2-63505008002*t+1) -3*(801771811*t^2+37868241988*t+1)/(t-1)/(t^2-63505008002*t+1) 25*(19889743*t^2-4660291400*t+1)/(t-1)/(t^2-63505008002*t+1) Then for all i>=0 we have 3 3 3 22 a(i) + 31 b(i) + 31 c(i) = -594 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 427, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = ( / ----- i = 0 2 198375365439741226360870384903077733542112164608925221541043680450895811 t + 366301130665385219866440472916286909240473571050870907395585205721797018 t / 2 - 29) / ((t - 1) (t - / 44692807979757104223387395185714999791644459084935958987648122025633602 t + 1)) infinity ----- \ i ) b(i) t = - 2 ( / ----- i = 0 2 87781235523162201973359255793085591371691212741837180263651851705426123 t + 80668013284866050690269882841519274184986587649956618218827885029044274 t / 2 + 3) / ((t - 1) (t - / 44692807979757104223387395185714999791644459084935958987648122025633602 t + 1)) infinity ----- \ i ) c(i) t = 4 ( / ----- i = 0 2 22908607955454625121587567954871112330429896652666884007292459651176007 t - 107133232359468751453402137272173545108768796848563783248532328018411214 t / 2 + 7) / ((t - 1) (t - / 44692807979757104223387395185714999791644459084935958987648122025633602 t + 1)) In Maple notation, these generating functions are (198375365439741226360870384903077733542112164608925221541043680450895811*t^2+ 366301130665385219866440472916286909240473571050870907395585205721797018*t-29)/ (t-1)/(t^2-\ 44692807979757104223387395185714999791644459084935958987648122025633602*t+1) -2*(87781235523162201973359255793085591371691212741837180263651851705426123*t^2 +80668013284866050690269882841519274184986587649956618218827885029044274*t+3)/( t-1)/(t^2-\ 44692807979757104223387395185714999791644459084935958987648122025633602*t+1) 4*(22908607955454625121587567954871112330429896652666884007292459651176007*t^2-\ 107133232359468751453402137272173545108768796848563783248532328018411214*t+7)/( t-1)/(t^2-\ 44692807979757104223387395185714999791644459084935958987648122025633602*t+1) Then for all i>=0 we have 3 3 3 22 a(i) + 37 b(i) + 37 c(i) = -267674 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 428, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 4 (96434931814589 t + 142918738840967 t - 6) ) a(i) t = --------------------------------------------- / 2 ----- (t - 1) (t - 70923380246402 t + 1) i = 0 infinity ----- 2 \ i 306801062406631 t + 299053761235568 t + 1 ) b(i) t = - ------------------------------------------ / 2 ----- (t - 1) (t - 70923380246402 t + 1) i = 0 infinity ----- 2 \ i 23 (5488784397251 t - 31830298468652 t + 1) ) c(i) t = -------------------------------------------- / 2 ----- (t - 1) (t - 70923380246402 t + 1) i = 0 In Maple notation, these generating functions are 4*(96434931814589*t^2+142918738840967*t-6)/(t-1)/(t^2-70923380246402*t+1) -(306801062406631*t^2+299053761235568*t+1)/(t-1)/(t^2-70923380246402*t+1) 23*(5488784397251*t^2-31830298468652*t+1)/(t-1)/(t^2-70923380246402*t+1) Then for all i>=0 we have 3 3 3 22 a(i) + 47 b(i) + 47 c(i) = -267674 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 429, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 4 (892233652388 t + 1414333788869 t - 7) ) a(i) t = ----------------------------------------- / 2 ----- (t - 1) (t - 650284185602 t + 1) i = 0 infinity ----- 2 \ i 3 (918793239391 t + 844207505608 t + 1) ) b(i) t = - ---------------------------------------- / 2 ----- (t - 1) (t - 650284185602 t + 1) i = 0 infinity ----- 2 \ i 25 (50997406531 t - 262557495932 t + 1) ) c(i) t = ---------------------------------------- / 2 ----- (t - 1) (t - 650284185602 t + 1) i = 0 In Maple notation, these generating functions are 4*(892233652388*t^2+1414333788869*t-7)/(t-1)/(t^2-650284185602*t+1) -3*(918793239391*t^2+844207505608*t+1)/(t-1)/(t^2-650284185602*t+1) 25*(50997406531*t^2-262557495932*t+1)/(t-1)/(t^2-650284185602*t+1) Then for all i>=0 we have 3 3 3 22 a(i) + 53 b(i) + 53 c(i) = -343750 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 430, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 1003159 t + 331296834 t - 25 ) a(i) t = ------------------------------ / 2 ----- (t - 1) (t - 384238402 t + 1) i = 0 infinity ----- 2 \ i 963145 t + 315967286 t + 1 ) b(i) t = - ------------------------------ / 2 ----- (t - 1) (t - 384238402 t + 1) i = 0 infinity ----- 2 \ i 8 (9467 t - 39625774 t + 3) ) c(i) t = ------------------------------ / 2 ----- (t - 1) (t - 384238402 t + 1) i = 0 In Maple notation, these generating functions are (1003159*t^2+331296834*t-25)/(t-1)/(t^2-384238402*t+1) -(963145*t^2+315967286*t+1)/(t-1)/(t^2-384238402*t+1) 8*(9467*t^2-39625774*t+3)/(t-1)/(t^2-384238402*t+1) Then for all i>=0 we have 3 3 3 23 a(i) + 26 b(i) + 26 c(i) = -23 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 431, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 27 (173130695 t + 17373648314 t - 1) ) a(i) t = ------------------------------------- / 2 ----- (t - 1) (t - 303735458882 t + 1) i = 0 infinity ----- 2 \ i 2 (2165630689 t + 212216963038 t + 1) ) b(i) t = - -------------------------------------- / 2 ----- (t - 1) (t - 303735458882 t + 1) i = 0 infinity ----- 2 \ i 623876497 t - 429389063978 t + 25 ) c(i) t = ---------------------------------- / 2 ----- (t - 1) (t - 303735458882 t + 1) i = 0 In Maple notation, these generating functions are 27*(173130695*t^2+17373648314*t-1)/(t-1)/(t^2-303735458882*t+1) -2*(2165630689*t^2+212216963038*t+1)/(t-1)/(t^2-303735458882*t+1) (623876497*t^2-429389063978*t+25)/(t-1)/(t^2-303735458882*t+1) Then for all i>=0 we have 3 3 3 23 a(i) + 29 b(i) + 29 c(i) = -184 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 432, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 10 (3771650609665 t + 22833920842018 t - 3) ) a(i) t = -------------------------------------------- / 2 ----- (t - 1) (t - 33247886145602 t + 1) i = 0 infinity ----- 2 \ i 2 (15534704102501 t + 77839710963898 t + 1) ) b(i) t = - -------------------------------------------- / 2 ----- (t - 1) (t - 33247886145602 t + 1) i = 0 infinity ----- 2 \ i 5 (2179092616709 t - 39528858643274 t + 5) ) c(i) t = ------------------------------------------- / 2 ----- (t - 1) (t - 33247886145602 t + 1) i = 0 In Maple notation, these generating functions are 10*(3771650609665*t^2+22833920842018*t-3)/(t-1)/(t^2-33247886145602*t+1) -2*(15534704102501*t^2+77839710963898*t+1)/(t-1)/(t^2-33247886145602*t+1) 5*(2179092616709*t^2-39528858643274*t+5)/(t-1)/(t^2-33247886145602*t+1) Then for all i>=0 we have 3 3 3 23 a(i) + 43 b(i) + 43 c(i) = -50531 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 433, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 2 ( / ----- i = 0 2 514562505303888906395700869773 t + 1942924623433040423811505590178 t - 15) / 2 / ((t - 1) (t - 485483669922773682113491576898 t + 1)) / infinity ----- \ i ) b(i) t = - 2 / ----- i = 0 2 (413956166470674558203540033341 t + 1197046614708598095498091369442 t + 1) / 2 / ((t - 1) (t - 485483669922773682113491576898 t + 1)) / infinity ----- \ i ) c(i) t = ( / ----- i = 0 2 324297966048181250572989853721 t - 3546303528406726557976252659314 t + 25) / 2 / ((t - 1) (t - 485483669922773682113491576898 t + 1)) / In Maple notation, these generating functions are 2*(514562505303888906395700869773*t^2+1942924623433040423811505590178*t-15)/(t-\ 1)/(t^2-485483669922773682113491576898*t+1) -2*(413956166470674558203540033341*t^2+1197046614708598095498091369442*t+1)/(t-\ 1)/(t^2-485483669922773682113491576898*t+1) (324297966048181250572989853721*t^2-3546303528406726557976252659314*t+25)/(t-1) /(t^2-485483669922773682113491576898*t+1) Then for all i>=0 we have 3 3 3 23 a(i) + 47 b(i) + 47 c(i) = -112999 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 434, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 399054463299730330117 t + 610649155801317252310 t - 27 ) a(i) t = ------------------------------------------------------- / 2 ----- (t - 1) (t - 69980267001465228098 t + 1) i = 0 infinity ----- 2 \ i 2 (156470912455469043329 t + 148634071992447305470 t + 1) ) b(i) t = - ---------------------------------------------------------- / 2 ----- (t - 1) (t - 69980267001465228098 t + 1) i = 0 infinity ----- 2 \ i 25 (5457478645749986857 t - 29865877401583294762 t + 1) ) c(i) t = -------------------------------------------------------- / 2 ----- (t - 1) (t - 69980267001465228098 t + 1) i = 0 In Maple notation, these generating functions are (399054463299730330117*t^2+610649155801317252310*t-27)/(t-1)/(t^2-\ 69980267001465228098*t+1) -2*(156470912455469043329*t^2+148634071992447305470*t+1)/(t-1)/(t^2-\ 69980267001465228098*t+1) 25*(5457478645749986857*t^2-29865877401583294762*t+1)/(t-1)/(t^2-\ 69980267001465228098*t+1) Then for all i>=0 we have 3 3 3 23 a(i) + 52 b(i) + 52 c(i) = -359375 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 435, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 12651887106154499251 t + 19973686111757118826 t - 29 ) a(i) t = ----------------------------------------------------- / 2 ----- (t - 1) (t - 2206966850845085954 t + 1) i = 0 infinity ----- 2 \ i 3 (3262835430279592177 t + 3010359602500191502 t + 1) ) b(i) t = - ------------------------------------------------------ / 2 ----- (t - 1) (t - 2206966850845085954 t + 1) i = 0 infinity ----- 2 \ i 26 (172989120667537921 t - 896819316757512962 t + 1) ) c(i) t = ----------------------------------------------------- / 2 ----- (t - 1) (t - 2206966850845085954 t + 1) i = 0 In Maple notation, these generating functions are (12651887106154499251*t^2+19973686111757118826*t-29)/(t-1)/(t^2-\ 2206966850845085954*t+1) -3*(3262835430279592177*t^2+3010359602500191502*t+1)/(t-1)/(t^2-\ 2206966850845085954*t+1) 26*(172989120667537921*t^2-896819316757512962*t+1)/(t-1)/(t^2-\ 2206966850845085954*t+1) Then for all i>=0 we have 3 3 3 23 a(i) + 55 b(i) + 55 c(i) = -404248 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 436, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2714094099341 t + 8105149294406 t - 19 ) a(i) t = --------------------------------------- / 2 ----- (t - 1) (t - 1835575167554 t + 1) i = 0 infinity ----- 2 \ i 6 (428400628593 t + 605285045966 t + 1) ) b(i) t = - ---------------------------------------- / 2 ----- (t - 1) (t - 1835575167554 t + 1) i = 0 infinity ----- 2 \ i 6 (247461021971 t - 1281146696534 t + 3) ) c(i) t = ----------------------------------------- / 2 ----- (t - 1) (t - 1835575167554 t + 1) i = 0 In Maple notation, these generating functions are (2714094099341*t^2+8105149294406*t-19)/(t-1)/(t^2-1835575167554*t+1) -6*(428400628593*t^2+605285045966*t+1)/(t-1)/(t^2-1835575167554*t+1) 6*(247461021971*t^2-1281146696534*t+3)/(t-1)/(t^2-1835575167554*t+1) Then for all i>=0 we have 3 3 3 24 a(i) + 35 b(i) + 35 c(i) = -31944 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 437, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 11 (31370722926567642071 t + 39785457596825122730 t - 1) ) a(i) t = --------------------------------------------------------- / 2 ----- (t - 1) (t - 152396499470363244098 t + 1) i = 0 infinity ----- 2 \ i 6 (58022327590742883369 t - 3101304246434482090 t + 1) ) b(i) t = - ------------------------------------------------------- / 2 ----- (t - 1) (t - 152396499470363244098 t + 1) i = 0 infinity ----- 2 \ i 12 (20795022076508487809 t - 48255533748662688450 t + 1) ) c(i) t = --------------------------------------------------------- / 2 ----- (t - 1) (t - 152396499470363244098 t + 1) i = 0 In Maple notation, these generating functions are 11*(31370722926567642071*t^2+39785457596825122730*t-1)/(t-1)/(t^2-\ 152396499470363244098*t+1) -6*(58022327590742883369*t^2-3101304246434482090*t+1)/(t-1)/(t^2-\ 152396499470363244098*t+1) 12*(20795022076508487809*t^2-48255533748662688450*t+1)/(t-1)/(t^2-\ 152396499470363244098*t+1) Then for all i>=0 we have 3 3 3 24 a(i) + 37 b(i) + 37 c(i) = -24000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 438, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 6706609773179 t + 16962712723346 t - 13 ) a(i) t = ---------------------------------------- / 2 ----- (t - 1) (t - 5735670545474 t + 1) i = 0 infinity ----- 2 \ i 6 (1056936618585 t + 599127354278 t + 1) ) b(i) t = - ----------------------------------------- / 2 ----- (t - 1) (t - 5735670545474 t + 1) i = 0 infinity ----- 2 \ i 12 (368787124217 t - 1196819110650 t + 1) ) c(i) t = ------------------------------------------ / 2 ----- (t - 1) (t - 5735670545474 t + 1) i = 0 In Maple notation, these generating functions are (6706609773179*t^2+16962712723346*t-13)/(t-1)/(t^2-5735670545474*t+1) -6*(1056936618585*t^2+599127354278*t+1)/(t-1)/(t^2-5735670545474*t+1) 12*(368787124217*t^2-1196819110650*t+1)/(t-1)/(t^2-5735670545474*t+1) Then for all i>=0 we have 3 3 3 24 a(i) + 43 b(i) + 43 c(i) = -12288 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 439, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 14 (1436007875726950533592656478336338992886995 t / ----- i = 0 / + 5057800376321847848827448057453977332724814 t - 1) / ((t - 1) / 2 (t - 25069120228839547243761333789330058373292098 t + 1)) infinity ----- \ i 2 ) b(i) t = - 6 (2996427299501039368655807489985411937382785 t / ----- i = 0 / + 3346362155988484632777782986833036566703166 t + 1) / ((t - 1) / 2 (t - 25069120228839547243761333789330058373292098 t + 1)) infinity ----- \ i 2 ) c(i) t = 12 (1019544357841536173130351585547259637729061 t / ----- i = 0 / - 4190939085586298173847146823956483889772038 t + 1) / ((t - 1) / 2 (t - 25069120228839547243761333789330058373292098 t + 1)) In Maple notation, these generating functions are 14*(1436007875726950533592656478336338992886995*t^2+ 5057800376321847848827448057453977332724814*t-1)/(t-1)/(t^2-\ 25069120228839547243761333789330058373292098*t+1) -6*(2996427299501039368655807489985411937382785*t^2+ 3346362155988484632777782986833036566703166*t+1)/(t-1)/(t^2-\ 25069120228839547243761333789330058373292098*t+1) 12*(1019544357841536173130351585547259637729061*t^2-\ 4190939085586298173847146823956483889772038*t+1)/(t-1)/(t^2-\ 25069120228839547243761333789330058373292098*t+1) Then for all i>=0 we have 3 3 3 24 a(i) + 49 b(i) + 49 c(i) = -8232 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 440, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (27514058064689908764234731680223377 t / ----- i = 0 / + 114628004901653380482244092265822726 t - 23) / ((t - 1) / 2 (t - 28021184309190457429899304311328322 t + 1)) infinity ----- \ i 2 ) b(i) t = - 12 (1937479650609385722052674948242161 t / ----- i = 0 / + 1262171152862189001776657377964878 t + 1) / ((t - 1) / 2 (t - 28021184309190457429899304311328322 t + 1)) infinity ----- \ i 2 ) c(i) t = 18 (1013733321975045948396381968724841 t / ----- i = 0 / - 3146833857622762430949270186196202 t + 1) / ((t - 1) / 2 (t - 28021184309190457429899304311328322 t + 1)) In Maple notation, these generating functions are (27514058064689908764234731680223377*t^2+114628004901653380482244092265822726*t -23)/(t-1)/(t^2-28021184309190457429899304311328322*t+1) -12*(1937479650609385722052674948242161*t^2+1262171152862189001776657377964878* t+1)/(t-1)/(t^2-28021184309190457429899304311328322*t+1) 18*(1013733321975045948396381968724841*t^2-3146833857622762430949270186196202*t +1)/(t-1)/(t^2-28021184309190457429899304311328322*t+1) Then for all i>=0 we have 3 3 3 24 a(i) + 77 b(i) + 77 c(i) = -24000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 441, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 2 ( / ----- i = 0 2 1039368870820739721128663155144626583913508894278580137180576211889 t + 1721757570434967840074553689946270907788688380225046632324646841722 t / 2 - 11) / ((t - 1) (t / - 642995510488884597706020769018690307164848843898349910833675841602 t + 1 )) infinity ----- \ i ) b(i) t = - 12 ( / ----- i = 0 2 144047220393570036853313310619564652566541955942476690278959384101 t - 38578139875477387600692882648413817917780257895815138848299541702 t + 1) / 2 / ((t - 1) (t / - 642995510488884597706020769018690307164848843898349910833675841602 t + 1 )) infinity ----- \ i ) c(i) t = 6 ( / ----- i = 0 2 234793473052743164930797741488122813650339866024513373523017424003 t - 445731634088928463436038597430424482947863262117836476384337108806 t + 3 / 2 ) / ((t - 1) (t / - 642995510488884597706020769018690307164848843898349910833675841602 t + 1 )) In Maple notation, these generating functions are 2*(1039368870820739721128663155144626583913508894278580137180576211889*t^2+ 1721757570434967840074553689946270907788688380225046632324646841722*t-11)/(t-1) /(t^2-642995510488884597706020769018690307164848843898349910833675841602*t+1) -12*(144047220393570036853313310619564652566541955942476690278959384101*t^2-\ 38578139875477387600692882648413817917780257895815138848299541702*t+1)/(t-1)/(t ^2-642995510488884597706020769018690307164848843898349910833675841602*t+1) 6*(234793473052743164930797741488122813650339866024513373523017424003*t^2-\ 445731634088928463436038597430424482947863262117836476384337108806*t+3)/(t-1)/( t^2-642995510488884597706020769018690307164848843898349910833675841602*t+1) Then for all i>=0 we have 3 3 3 24 a(i) + 91 b(i) + 91 c(i) = -117912 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 442, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 21 (958401599 t + 1398571202 t - 1) ) a(i) t = ------------------------------------ / 2 ----- (t - 1) (t - 4733164802 t + 1) i = 0 infinity ----- 2 \ i 5 (4176327121 t + 2795000878 t + 1) ) b(i) t = - ------------------------------------ / 2 ----- (t - 1) (t - 4733164802 t + 1) i = 0 infinity ----- 2 \ i 25 (432736753 t - 1827002354 t + 1) ) c(i) t = ------------------------------------ / 2 ----- (t - 1) (t - 4733164802 t + 1) i = 0 In Maple notation, these generating functions are 21*(958401599*t^2+1398571202*t-1)/(t-1)/(t^2-4733164802*t+1) -5*(4176327121*t^2+2795000878*t+1)/(t-1)/(t^2-4733164802*t+1) 25*(432736753*t^2-1827002354*t+1)/(t-1)/(t^2-4733164802*t+1) Then for all i>=0 we have 3 3 3 25 a(i) + 26 b(i) + 26 c(i) = -171475 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 443, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 9 (1010039399 t + 2234539802 t - 1) ) a(i) t = ------------------------------------ / 2 ----- (t - 1) (t - 9447451202 t + 1) i = 0 infinity ----- 2 \ i 5 (2043682201 t + 819181798 t + 1) ) b(i) t = - ----------------------------------- / 2 ----- (t - 1) (t - 9447451202 t + 1) i = 0 infinity ----- 2 \ i 10 (718829281 t - 2150261282 t + 1) ) c(i) t = ------------------------------------ / 2 ----- (t - 1) (t - 9447451202 t + 1) i = 0 In Maple notation, these generating functions are 9*(1010039399*t^2+2234539802*t-1)/(t-1)/(t^2-9447451202*t+1) -5*(2043682201*t^2+819181798*t+1)/(t-1)/(t^2-9447451202*t+1) 10*(718829281*t^2-2150261282*t+1)/(t-1)/(t^2-9447451202*t+1) Then for all i>=0 we have 3 3 3 25 a(i) + 27 b(i) + 27 c(i) = -5400 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 444, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 9 (148957 t + 57161446 t - 3) ) a(i) t = ------------------------------ / 2 ----- (t - 1) (t - 590587202 t + 1) i = 0 infinity ----- 2 \ i 1291081 t + 492628918 t + 1 ) b(i) t = - ------------------------------ / 2 ----- (t - 1) (t - 590587202 t + 1) i = 0 infinity ----- 2 \ i 2 (47053 t - 247007066 t + 13) ) c(i) t = ------------------------------- / 2 ----- (t - 1) (t - 590587202 t + 1) i = 0 In Maple notation, these generating functions are 9*(148957*t^2+57161446*t-3)/(t-1)/(t^2-590587202*t+1) -(1291081*t^2+492628918*t+1)/(t-1)/(t^2-590587202*t+1) 2*(47053*t^2-247007066*t+13)/(t-1)/(t^2-590587202*t+1) Then for all i>=0 we have 3 3 3 25 a(i) + 28 b(i) + 28 c(i) = -25 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 445, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 924009457910933891 t + 106340606928851869338 t - 29 ) a(i) t = ---------------------------------------------------- / 2 ----- (t - 1) (t - 67782646279738803202 t + 1) i = 0 infinity ----- 2 \ i 2 (430384817612977921 t + 48527258115096782078 t + 1) ) b(i) t = - ------------------------------------------------------ / 2 ----- (t - 1) (t - 67782646279738803202 t + 1) i = 0 infinity ----- 2 \ i 115600717555847867 t - 98030886582975367894 t + 27 ) c(i) t = --------------------------------------------------- / 2 ----- (t - 1) (t - 67782646279738803202 t + 1) i = 0 In Maple notation, these generating functions are (924009457910933891*t^2+106340606928851869338*t-29)/(t-1)/(t^2-\ 67782646279738803202*t+1) -2*(430384817612977921*t^2+48527258115096782078*t+1)/(t-1)/(t^2-\ 67782646279738803202*t+1) (115600717555847867*t^2-98030886582975367894*t+27)/(t-1)/(t^2-\ 67782646279738803202*t+1) Then for all i>=0 we have 3 3 3 25 a(i) + 31 b(i) + 31 c(i) = -200 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 446, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (19820404089567187 t + 58782750721794426 t - 13) ) a(i) t = --------------------------------------------------- / 2 ----- (t - 1) (t - 22415987969211202 t + 1) i = 0 infinity ----- 2 \ i 10 (5967624571865603 t - 3023686189417606 t + 3) ) b(i) t = - ------------------------------------------------- / 2 ----- (t - 1) (t - 22415987969211202 t + 1) i = 0 infinity ----- 2 \ i 35 (1563461277036121 t - 2404586529164122 t + 1) ) c(i) t = ------------------------------------------------- / 2 ----- (t - 1) (t - 22415987969211202 t + 1) i = 0 In Maple notation, these generating functions are 2*(19820404089567187*t^2+58782750721794426*t-13)/(t-1)/(t^2-22415987969211202*t +1) -10*(5967624571865603*t^2-3023686189417606*t+3)/(t-1)/(t^2-22415987969211202*t+ 1) 35*(1563461277036121*t^2-2404586529164122*t+1)/(t-1)/(t^2-22415987969211202*t+1 ) Then for all i>=0 we have 3 3 3 25 a(i) + 32 b(i) + 32 c(i) = -68600 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 447, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (3773106873036849587 t + 60933703661115028826 t - 13) ) a(i) t = -------------------------------------------------------- / 2 ----- (t - 1) (t - 62185765967886220802 t + 1) i = 0 infinity ----- 2 \ i 5 (1500829930441234963 t + 11104392900887053034 t + 3) ) b(i) t = - ------------------------------------------------------- / 2 ----- (t - 1) (t - 62185765967886220802 t + 1) i = 0 infinity ----- 2 \ i 25 (199549802807264337 t - 2720594369072921938 t + 1) ) c(i) t = ------------------------------------------------------ / 2 ----- (t - 1) (t - 62185765967886220802 t + 1) i = 0 In Maple notation, these generating functions are 2*(3773106873036849587*t^2+60933703661115028826*t-13)/(t-1)/(t^2-\ 62185765967886220802*t+1) -5*(1500829930441234963*t^2+11104392900887053034*t+3)/(t-1)/(t^2-\ 62185765967886220802*t+1) 25*(199549802807264337*t^2-2720594369072921938*t+1)/(t-1)/(t^2-\ 62185765967886220802*t+1) Then for all i>=0 we have 3 3 3 25 a(i) + 36 b(i) + 36 c(i) = -1600 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 448, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (13905647639305520987865780904069804787970095030383 t / ----- i = 0 / + 230779763749872573408087728646390735764346302851234 t - 17) / ((t - 1) / 2 (t - 141895192906053050174822354853463418493809052652802 t + 1)) infinity ----- \ i 2 ) b(i) t = - 5 (2492854341073276452162660857643193738745297097841 t / ----- i = 0 / + 31025695164293585793858367847899346062941880694158 t + 1) / ((t - 1) / 2 (t - 141895192906053050174822354853463418493809052652802 t + 1)) infinity ----- \ i 2 ) c(i) t = 15 (367429859047574784458694255745404419982762531601 t / ----- i = 0 / - 11540279694169862199799037157592917687211821795602 t + 1) / ((t - 1) / 2 (t - 141895192906053050174822354853463418493809052652802 t + 1)) In Maple notation, these generating functions are (13905647639305520987865780904069804787970095030383*t^2+ 230779763749872573408087728646390735764346302851234*t-17)/(t-1)/(t^2-\ 141895192906053050174822354853463418493809052652802*t+1) -5*(2492854341073276452162660857643193738745297097841*t^2+ 31025695164293585793858367847899346062941880694158*t+1)/(t-1)/(t^2-\ 141895192906053050174822354853463418493809052652802*t+1) 15*(367429859047574784458694255745404419982762531601*t^2-\ 11540279694169862199799037157592917687211821795602*t+1)/(t-1)/(t^2-\ 141895192906053050174822354853463418493809052652802*t+1) Then for all i>=0 we have 3 3 3 25 a(i) + 38 b(i) + 38 c(i) = -675 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 449, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 50566690245735558491938964977 t + 60033231265358982605347035046 t - 23 ----------------------------------------------------------------------- 2 (t - 1) (t - 9631075042248268010337000002 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 10 (4862007478872013047259806001 t + 512718728470594241485193998 t + 1) - ------------------------------------------------------------------------ 2 (t - 1) (t - 9631075042248268010337000002 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 25 (1270580454938997772344736201 t - 3420470937876040687842736202 t + 1) ------------------------------------------------------------------------- 2 (t - 1) (t - 9631075042248268010337000002 t + 1) In Maple notation, these generating functions are (50566690245735558491938964977*t^2+60033231265358982605347035046*t-23)/(t-1)/(t ^2-9631075042248268010337000002*t+1) -10*(4862007478872013047259806001*t^2+512718728470594241485193998*t+1)/(t-1)/(t ^2-9631075042248268010337000002*t+1) 25*(1270580454938997772344736201*t^2-3420470937876040687842736202*t+1)/(t-1)/(t ^2-9631075042248268010337000002*t+1) Then for all i>=0 we have 3 3 3 25 a(i) + 39 b(i) + 39 c(i) = -266200 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 450, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 28 ( / ----- i = 0 2 1281520838720266821740272172194973957112183894476878099 t / + 10939075259979466589865278875952204635728987879170925102 t - 1) / ( / (t - 1) 2 (t - 97346970632377363586464731426266414089982667461878227202 t + 1)) infinity ----- \ i ) b(i) t = - 25 ( / ----- i = 0 2 1667446997042405127788005404516682407686220918205642945 t / + 1257140103501120816869733307860420161540726172923745854 t + 1) / ( / (t - 1) 2 (t - 97346970632377363586464731426266414089982667461878227202 t + 1)) infinity ----- \ i ) c(i) t = 10 ( / ----- i = 0 2 3656009157117906090773904642413716436370678737723356123 t / - 10967476908476720952418251423356472859438046465546828126 t + 3) / ( / (t - 1) 2 (t - 97346970632377363586464731426266414089982667461878227202 t + 1)) In Maple notation, these generating functions are 28*(1281520838720266821740272172194973957112183894476878099*t^2+ 10939075259979466589865278875952204635728987879170925102*t-1)/(t-1)/(t^2-\ 97346970632377363586464731426266414089982667461878227202*t+1) -25*(1667446997042405127788005404516682407686220918205642945*t^2+ 1257140103501120816869733307860420161540726172923745854*t+1)/(t-1)/(t^2-\ 97346970632377363586464731426266414089982667461878227202*t+1) 10*(3656009157117906090773904642413716436370678737723356123*t^2-\ 10967476908476720952418251423356472859438046465546828126*t+3)/(t-1)/(t^2-\ 97346970632377363586464731426266414089982667461878227202*t+1) Then for all i>=0 we have 3 3 3 25 a(i) + 49 b(i) + 49 c(i) = -8575 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 451, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 9 (440625985084089162021430212414257466634274537717 t / ----- i = 0 / + 650163108597551471553171361453939719531702463886 t - 3) / ((t - 1) / 2 (t - 641760418792142577321929026373162330004464308802 t + 1)) infinity ----- \ i 2 ) b(i) t = - (3160261619453164242532990920734128872606709494361 t / ----- i = 0 / + 3090415911615343472689077204387568121640900185638 t + 1) / ((t - 1) / 2 (t - 641760418792142577321929026373162330004464308802 t + 1)) infinity ----- \ i 2 ) c(i) t = 26 (49603061819374196951688476782076125003950531361 t / ----- i = 0 / - 290013736091239878306383404671372163244243211362 t + 1) / ((t - 1) / 2 (t - 641760418792142577321929026373162330004464308802 t + 1)) In Maple notation, these generating functions are 9*(440625985084089162021430212414257466634274537717*t^2+ 650163108597551471553171361453939719531702463886*t-3)/(t-1)/(t^2-\ 641760418792142577321929026373162330004464308802*t+1) -(3160261619453164242532990920734128872606709494361*t^2+ 3090415911615343472689077204387568121640900185638*t+1)/(t-1)/(t^2-\ 641760418792142577321929026373162330004464308802*t+1) 26*(49603061819374196951688476782076125003950531361*t^2-\ 290013736091239878306383404671372163244243211362*t+1)/(t-1)/(t^2-\ 641760418792142577321929026373162330004464308802*t+1) Then for all i>=0 we have 3 3 3 25 a(i) + 53 b(i) + 53 c(i) = -439400 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 452, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 3 (7787024679593 t + 32720337766814 t - 7) ) a(i) t = ------------------------------------------- / 2 ----- (t - 1) (t - 26803379131202 t + 1) i = 0 infinity ----- 2 \ i 15 (1626522903721 t + 388768760278 t + 1) ) b(i) t = - ------------------------------------------ / 2 ----- (t - 1) (t - 26803379131202 t + 1) i = 0 infinity ----- 2 \ i 20 (1025216560801 t - 2536685308802 t + 1) ) c(i) t = ------------------------------------------- / 2 ----- (t - 1) (t - 26803379131202 t + 1) i = 0 In Maple notation, these generating functions are 3*(7787024679593*t^2+32720337766814*t-7)/(t-1)/(t^2-26803379131202*t+1) -15*(1626522903721*t^2+388768760278*t+1)/(t-1)/(t^2-26803379131202*t+1) 20*(1025216560801*t^2-2536685308802*t+1)/(t-1)/(t^2-26803379131202*t+1) Then for all i>=0 we have 3 3 3 25 a(i) + 54 b(i) + 54 c(i) = -18225 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 453, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 24287799532560607149091 t + 36973094071346142958138 t - 29 ) a(i) t = ----------------------------------------------------------- / 2 ----- (t - 1) (t - 3921020899397830267202 t + 1) i = 0 infinity ----- \ i ) b(i) t = / ----- i = 0 2 2 (9545076812287013649121 t + 9107652862673719310878 t + 1) - ------------------------------------------------------------ 2 (t - 1) (t - 3921020899397830267202 t + 1) infinity ----- 2 \ i 27 (305458739855906316121 t - 1687142419482627276122 t + 1) ) c(i) t = ------------------------------------------------------------ / 2 ----- (t - 1) (t - 3921020899397830267202 t + 1) i = 0 In Maple notation, these generating functions are (24287799532560607149091*t^2+36973094071346142958138*t-29)/(t-1)/(t^2-\ 3921020899397830267202*t+1) -2*(9545076812287013649121*t^2+9107652862673719310878*t+1)/(t-1)/(t^2-\ 3921020899397830267202*t+1) 27*(305458739855906316121*t^2-1687142419482627276122*t+1)/(t-1)/(t^2-\ 3921020899397830267202*t+1) Then for all i>=0 we have 3 3 3 25 a(i) + 56 b(i) + 56 c(i) = -492075 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 454, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 19 (481299762504014510679716975514410399 t / ----- i = 0 / + 1437314362604302893237391399112138402 t - 1) / ((t - 1) / 2 (t - 6184669852042850600814442571827444802 t + 1)) infinity ----- \ i 2 ) b(i) t = - 5 (1443425744198444189800302951361701841 t / ----- i = 0 / + 2039408814119202052979161295571842158 t + 1) / ((t - 1) / 2 (t - 6184669852042850600814442571827444802 t + 1)) infinity ----- \ i 2 ) c(i) t = 15 (277926459453341936535331594125594001 t / ----- i = 0 / - 1438871312225890684128486343103442002 t + 1) / ((t - 1) / 2 (t - 6184669852042850600814442571827444802 t + 1)) In Maple notation, these generating functions are 19*(481299762504014510679716975514410399*t^2+ 1437314362604302893237391399112138402*t-1)/(t-1)/(t^2-\ 6184669852042850600814442571827444802*t+1) -5*(1443425744198444189800302951361701841*t^2+ 2039408814119202052979161295571842158*t+1)/(t-1)/(t^2-\ 6184669852042850600814442571827444802*t+1) 15*(277926459453341936535331594125594001*t^2-\ 1438871312225890684128486343103442002*t+1)/(t-1)/(t^2-\ 6184669852042850600814442571827444802*t+1) Then for all i>=0 we have 3 3 3 25 a(i) + 63 b(i) + 63 c(i) = -33275 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 455, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 12 (851691449275404442070524171943299725599 t / ----- i = 0 / + 1884221984911558276099102478817298341602 t - 1) / ((t - 1) / 2 (t - 7966336176014979679376265836038212019202 t + 1)) infinity ----- \ i 2 ) b(i) t = - 5 (1723285900547619292677359734654910220001 t / ----- i = 0 / + 690755364911465458648781427780911603998 t + 1) / ((t - 1) / 2 (t - 7966336176014979679376265836038212019202 t + 1)) infinity ----- \ i 2 ) c(i) t = 10 (606135515491188313717522615744465192321 t / ----- i = 0 / - 1813156148220730689380593196962376104322 t + 1) / ((t - 1) / 2 (t - 7966336176014979679376265836038212019202 t + 1)) In Maple notation, these generating functions are 12*(851691449275404442070524171943299725599*t^2+ 1884221984911558276099102478817298341602*t-1)/(t-1)/(t^2-\ 7966336176014979679376265836038212019202*t+1) -5*(1723285900547619292677359734654910220001*t^2+ 690755364911465458648781427780911603998*t+1)/(t-1)/(t^2-\ 7966336176014979679376265836038212019202*t+1) 10*(606135515491188313717522615744465192321*t^2-\ 1813156148220730689380593196962376104322*t+1)/(t-1)/(t^2-\ 7966336176014979679376265836038212019202*t+1) Then for all i>=0 we have 3 3 3 25 a(i) + 64 b(i) + 64 c(i) = -12800 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 456, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 4 (9893 t + 352514 t - 7) ) a(i) t = ---------------------------- / 2 ----- (t - 1) (t - 1435202 t + 1) i = 0 infinity ----- 2 \ i 20 (1811 t + 16188 t + 1) ) b(i) t = - ---------------------------- / 2 ----- (t - 1) (t - 1435202 t + 1) i = 0 infinity ----- 2 \ i 25 (1185 t - 15586 t + 1) ) c(i) t = ---------------------------- / 2 ----- (t - 1) (t - 1435202 t + 1) i = 0 In Maple notation, these generating functions are 4*(9893*t^2+352514*t-7)/(t-1)/(t^2-1435202*t+1) -20*(1811*t^2+16188*t+1)/(t-1)/(t^2-1435202*t+1) 25*(1185*t^2-15586*t+1)/(t-1)/(t^2-1435202*t+1) Then for all i>=0 we have 3 3 3 25 a(i) + 72 b(i) + 72 c(i) = -200 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 457, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 27 (15306322698647744323447339805760382785680740005626413\ / ----- i = 0 2 90563982533410890600043319679 t + 2475616576372403839595867395317713915\ / 2 346483047056766557768889109199911222171061122 t - 1) / ((t - 1) (t - / 102647259749941268570893311717401071114378116338285550001992281654971520\ 48078572802 t + 1)) infinity ----- \ i ) b(i) t = - 30 (202540727344439500751585884868923468951433154834360\ / ----- i = 0 2 5983223751043003000813822302577 t - 11261629281019492371234360938123636\ / 2 93470200757798818012087164026819856807684973938 t + 1) / ((t - 1) (t - / 102647259749941268570893311717401071114378116338285550001992281654971520\ 48078572802 t + 1)) infinity ----- \ i ) c(i) t = 2 (269371864944701826399622312740424342159368067238881466\ / ----- i = 0 2 19587304944870508357237069379 t - 4042585167460686919584857259719549915\ / 2 6598768582059966186636110187617668449296998998 t + 19) / ((t - 1) (t - / 102647259749941268570893311717401071114378116338285550001992281654971520\ 48078572802 t + 1)) In Maple notation, these generating functions are 27*(153063226986477443234473398057603827856807400056264139056398253341089060004\ 3319679*t^2+2475616576372403839595867395317713915346483047056766557768889109199\ 911222171061122*t-1)/(t-1)/(t^2-10264725974994126857089331171740107111437811633\ 828555000199228165497152048078572802*t+1) -30*(20254072734443950075158588486892346895143315483436059832237510430030008138\ 22302577*t^2-112616292810194923712343609381236369347020075779881801208716402681\ 9856807684973938*t+1)/(t-1)/(t^2-1026472597499412685708933117174010711143781163\ 3828555000199228165497152048078572802*t+1) 2*(2693718649447018263996223127404243421593680672388814661958730494487050835723\ 7069379*t^2-4042585167460686919584857259719549915659876858205996618663611018761\ 7668449296998998*t+19)/(t-1)/(t^2-102647259749941268570893311717401071114378116\ 33828555000199228165497152048078572802*t+1) Then for all i>=0 we have 3 3 3 26 a(i) + 27 b(i) + 27 c(i) = -240786 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 458, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 4 (428 t + 176429 t - 7) ) a(i) t = --------------------------- / 2 ----- (t - 1) (t - 806402 t + 1) i = 0 infinity ----- 2 \ i 1651 t + 676948 t + 1 ) b(i) t = - --------------------------- / 2 ----- (t - 1) (t - 806402 t + 1) i = 0 infinity ----- 2 \ i 9 (13 t - 75416 t + 3) ) c(i) t = --------------------------- / 2 ----- (t - 1) (t - 806402 t + 1) i = 0 In Maple notation, these generating functions are 4*(428*t^2+176429*t-7)/(t-1)/(t^2-806402*t+1) -(1651*t^2+676948*t+1)/(t-1)/(t^2-806402*t+1) 9*(13*t^2-75416*t+3)/(t-1)/(t^2-806402*t+1) Then for all i>=0 we have 3 3 3 26 a(i) + 29 b(i) + 29 c(i) = -26 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 459, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 18 / ----- i = 0 2 (57017786085563207374499103249 t + 81721684876413694282859015812 t - 1) / 2 / ((t - 1) (t - 331076837609074708958154143522 t + 1)) / infinity ----- \ i ) b(i) t = - ( / ----- i = 0 2 1325608338838943013424731378227 t - 647111698706969843951571533164 t + 17) / 2 / ((t - 1) (t - 331076837609074708958154143522 t + 1)) / infinity ----- \ i ) c(i) t = ( / ----- i = 0 2 1139004675286190698380916131233 t - 1817501315418163867854075976336 t + 23 / 2 ) / ((t - 1) (t - 331076837609074708958154143522 t + 1)) / In Maple notation, these generating functions are 18*(57017786085563207374499103249*t^2+81721684876413694282859015812*t-1)/(t-1)/ (t^2-331076837609074708958154143522*t+1) -(1325608338838943013424731378227*t^2-647111698706969843951571533164*t+17)/(t-1 )/(t^2-331076837609074708958154143522*t+1) (1139004675286190698380916131233*t^2-1817501315418163867854075976336*t+23)/(t-1 )/(t^2-331076837609074708958154143522*t+1) Then for all i>=0 we have 3 3 3 26 a(i) + 33 b(i) + 33 c(i) = -87750 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 460, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 3 (446327159571701791 t + 685087071597971018 t - 9) ) a(i) t = ---------------------------------------------------- / 2 ----- (t - 1) (t - 276867814938019202 t + 1) i = 0 infinity ----- 2 \ i 3 (436631364427363663 t + 214182131378200334 t + 3) ) b(i) t = - ---------------------------------------------------- / 2 ----- (t - 1) (t - 276867814938019202 t + 1) i = 0 infinity ----- 2 \ i 774301501796048849 t - 2726741989212740878 t + 29 ) c(i) t = -------------------------------------------------- / 2 ----- (t - 1) (t - 276867814938019202 t + 1) i = 0 In Maple notation, these generating functions are 3*(446327159571701791*t^2+685087071597971018*t-9)/(t-1)/(t^2-276867814938019202 *t+1) -3*(436631364427363663*t^2+214182131378200334*t+3)/(t-1)/(t^2-\ 276867814938019202*t+1) (774301501796048849*t^2-2726741989212740878*t+29)/(t-1)/(t^2-276867814938019202 *t+1) Then for all i>=0 we have 3 3 3 26 a(i) + 35 b(i) + 35 c(i) = -316342 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 461, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 28 (124875134 t + 184029869 t - 1) ) a(i) t = ----------------------------------- / 2 ----- (t - 1) (t - 544102274 t + 1) i = 0 infinity ----- 2 \ i 2787952987 t + 2728798252 t + 1 ) b(i) t = - -------------------------------- / 2 ----- (t - 1) (t - 544102274 t + 1) i = 0 infinity ----- 2 \ i 27 (42039271 t - 246363392 t + 1) ) c(i) t = ---------------------------------- / 2 ----- (t - 1) (t - 544102274 t + 1) i = 0 In Maple notation, these generating functions are 28*(124875134*t^2+184029869*t-1)/(t-1)/(t^2-544102274*t+1) -(2787952987*t^2+2728798252*t+1)/(t-1)/(t^2-544102274*t+1) 27*(42039271*t^2-246363392*t+1)/(t-1)/(t^2-544102274*t+1) Then for all i>=0 we have 3 3 3 26 a(i) + 55 b(i) + 55 c(i) = -511758 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 462, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (363904168794006941409608842204394046119497 t / ----- i = 0 / + 1010863823836177464994754351829516887779726 t - 23) / ((t - 1) / 2 (t - 209900900201452346356920392817499964539202 t + 1)) infinity ----- \ i 2 ) b(i) t = - 16 (23591330804157526806089486558344688688931 t / ----- i = 0 / - 2219040724735313738150276659066509142532 t + 1) / ((t - 1) / 2 (t - 209900900201452346356920392817499964539202 t + 1)) infinity ----- \ i 2 ) c(i) t = 2 (158405299033759635997915155616391339001491 t / ----- i = 0 / - 329383619669137340541428834810616775372702 t + 11) / ((t - 1) / 2 (t - 209900900201452346356920392817499964539202 t + 1)) In Maple notation, these generating functions are (363904168794006941409608842204394046119497*t^2+ 1010863823836177464994754351829516887779726*t-23)/(t-1)/(t^2-\ 209900900201452346356920392817499964539202*t+1) -16*(23591330804157526806089486558344688688931*t^2-\ 2219040724735313738150276659066509142532*t+1)/(t-1)/(t^2-\ 209900900201452346356920392817499964539202*t+1) 2*(158405299033759635997915155616391339001491*t^2-\ 329383619669137340541428834810616775372702*t+11)/(t-1)/(t^2-\ 209900900201452346356920392817499964539202*t+1) Then for all i>=0 we have 3 3 3 26 a(i) + 57 b(i) + 57 c(i) = -57122 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 463, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 26 (894224159544852218064316431941305449915815999 t / ----- i = 0 / + 61976977839342042254372570672475678905517624002 t - 1) / ((t - 1) / 2 (t - 3204958218484963415318450949750186141575197440002 t + 1)) infinity ----- \ i 2 ) b(i) t = - (20815277313461014306927956396394573372914594017 t / ----- i = 0 / + 516919108292763726982162045210830730495581725966 t + 17) / ((t - 1) / 2 (t - 3204958218484963415318450949750186141575197440002 t + 1)) infinity ----- \ i 2 ) c(i) t = (15648648836090757047000794789622586328956546023 t / ----- i = 0 / - 553383034442315498336090796396847890197452866046 t + 23) / ((t - 1) / 2 (t - 3204958218484963415318450949750186141575197440002 t + 1)) In Maple notation, these generating functions are 26*(894224159544852218064316431941305449915815999*t^2+ 61976977839342042254372570672475678905517624002*t-1)/(t-1)/(t^2-\ 3204958218484963415318450949750186141575197440002*t+1) -(20815277313461014306927956396394573372914594017*t^2+ 516919108292763726982162045210830730495581725966*t+17)/(t-1)/(t^2-\ 3204958218484963415318450949750186141575197440002*t+1) (15648648836090757047000794789622586328956546023*t^2-\ 553383034442315498336090796396847890197452866046*t+23)/(t-1)/(t^2-\ 3204958218484963415318450949750186141575197440002*t+1) Then for all i>=0 we have 3 3 3 26 a(i) + 63 b(i) + 63 c(i) = -26 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 464, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 5 ( / ----- i = 0 2 8053606119149916135802725732952383444809716549554917083 t / + 34082742399210731601520138770654206585929826810884735882 t - 5) / ( / (t - 1) 2 (t - 31677134125494343020605855925344720944933508176232606402 t + 1)) infinity ----- \ i ) b(i) t = - 5 ( / ----- i = 0 2 6149617881208368325955459113784095688448378355910860537 t / + 16205254900868104563434768753000700043715398424731986982 t + 1) / ( / (t - 1) 2 (t - 31677134125494343020605855925344720944933508176232606402 t + 1)) infinity ----- \ i 2 ) c(i) t = (15511537288731189480961327966037590843953238847963919019 t / ----- i = 0 / - 127285901199113553927912467299961569504772122751178156638 t + 19) / ( / (t - 1) 2 (t - 31677134125494343020605855925344720944933508176232606402 t + 1)) In Maple notation, these generating functions are 5*(8053606119149916135802725732952383444809716549554917083*t^2+ 34082742399210731601520138770654206585929826810884735882*t-5)/(t-1)/(t^2-\ 31677134125494343020605855925344720944933508176232606402*t+1) -5*(6149617881208368325955459113784095688448378355910860537*t^2+ 16205254900868104563434768753000700043715398424731986982*t+1)/(t-1)/(t^2-\ 31677134125494343020605855925344720944933508176232606402*t+1) (15511537288731189480961327966037590843953238847963919019*t^2-\ 127285901199113553927912467299961569504772122751178156638*t+19)/(t-1)/(t^2-\ 31677134125494343020605855925344720944933508176232606402*t+1) Then for all i>=0 we have 3 3 3 26 a(i) + 67 b(i) + 67 c(i) = -44928 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 465, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 21393301837845155 t + 43116502880411882 t - 13 ) a(i) t = ----------------------------------------------- / 2 ----- (t - 1) (t - 14145817291716098 t + 1) i = 0 infinity ----- 2 \ i 18739511376789247 t - 1301133163725446 t + 7 ) b(i) t = - --------------------------------------------- / 2 ----- (t - 1) (t - 14145817291716098 t + 1) i = 0 infinity ----- 2 \ i 14849820133544675 t - 32288198346608494 t + 11 ) c(i) t = ----------------------------------------------- / 2 ----- (t - 1) (t - 14145817291716098 t + 1) i = 0 In Maple notation, these generating functions are (21393301837845155*t^2+43116502880411882*t-13)/(t-1)/(t^2-14145817291716098*t+1 ) -(18739511376789247*t^2-1301133163725446*t+7)/(t-1)/(t^2-14145817291716098*t+1) (14849820133544675*t^2-32288198346608494*t+11)/(t-1)/(t^2-14145817291716098*t+1 ) Then for all i>=0 we have 3 3 3 26 a(i) + 77 b(i) + 77 c(i) = -18954 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 466, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 11529772175402780263295210851 t + 169014266360607175598153551546 t - 29 ------------------------------------------------------------------------ 2 (t - 1) (t - 50731382729126764456936015874 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 7648817049329804784383691749 t + 89337649932824303736229279766 t + 5 - --------------------------------------------------------------------- 2 (t - 1) (t - 50731382729126764456936015874 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 3036908179168692679065607411 t - 100023375161322801199678578950 t + 19 ----------------------------------------------------------------------- 2 (t - 1) (t - 50731382729126764456936015874 t + 1) In Maple notation, these generating functions are (11529772175402780263295210851*t^2+169014266360607175598153551546*t-29)/(t-1)/( t^2-50731382729126764456936015874*t+1) -(7648817049329804784383691749*t^2+89337649932824303736229279766*t+5)/(t-1)/(t^ 2-50731382729126764456936015874*t+1) (3036908179168692679065607411*t^2-100023375161322801199678578950*t+19)/(t-1)/(t ^2-50731382729126764456936015874*t+1) Then for all i>=0 we have 3 3 3 26 a(i) + 95 b(i) + 95 c(i) = -5616 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 467, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (13124021 t + 101482988 t - 13) ) a(i) t = ---------------------------------- / 2 ----- (t - 1) (t - 65448098 t + 1) i = 0 infinity ----- 2 \ i 32338277 t - 11509496 t + 27 ) b(i) t = - ----------------------------- / 2 ----- (t - 1) (t - 65448098 t + 1) i = 0 infinity ----- 2 \ i 30747487 t - 51576324 t + 29 ) c(i) t = ----------------------------- / 2 ----- (t - 1) (t - 65448098 t + 1) i = 0 In Maple notation, these generating functions are 2*(13124021*t^2+101482988*t-13)/(t-1)/(t^2-65448098*t+1) -(32338277*t^2-11509496*t+27)/(t-1)/(t^2-65448098*t+1) (30747487*t^2-51576324*t+29)/(t-1)/(t^2-65448098*t+1) Then for all i>=0 we have 3 3 3 26 a(i) + 99 b(i) + 99 c(i) = -8918 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 468, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 5 ( / ----- i = 0 2 335632699603544375063477260596878676305993025835316296081063579 t + 6996637369729640247722431894195473618019660611617645106816237226 t - 5) / 2 / ((t - 1) (t / - 23820300570069875644975330786049554109778952099102671893007009602 t + 1) ) infinity ----- \ i ) b(i) t = - ( / ----- i = 0 2 1940628491997851151576203505358340675396725034904098705630051899 t + 15436162017142862249132722265873691721186955685830819227255087282 t + 19 / 2 ) / ((t - 1) (t / - 23820300570069875644975330786049554109778952099102671893007009602 t + 1) ) infinity ----- \ i ) c(i) t = 28 ( / ----- i = 0 2 50043528435944305314129108958130100098646192365721339839277541 t - 670643189476684069625162172216416971405206218106254123156603942 t + 1) / 2 / ((t - 1) (t / - 23820300570069875644975330786049554109778952099102671893007009602 t + 1) ) In Maple notation, these generating functions are 5*(335632699603544375063477260596878676305993025835316296081063579*t^2+ 6996637369729640247722431894195473618019660611617645106816237226*t-5)/(t-1)/(t^ 2-23820300570069875644975330786049554109778952099102671893007009602*t+1) -(1940628491997851151576203505358340675396725034904098705630051899*t^2+ 15436162017142862249132722265873691721186955685830819227255087282*t+19)/(t-1)/( t^2-23820300570069875644975330786049554109778952099102671893007009602*t+1) 28*(50043528435944305314129108958130100098646192365721339839277541*t^2-\ 670643189476684069625162172216416971405206218106254123156603942*t+1)/(t-1)/(t^2 -23820300570069875644975330786049554109778952099102671893007009602*t+1) Then for all i>=0 we have 3 3 3 27 a(i) + 28 b(i) + 28 c(i) = -729 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 469, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 2 ( / ----- i = 0 2 134973255590817393334452185246448590227620809903875134270731 t + 2929831530019758929168505764405175090083008241386782543543938 t - 13) / / ((t - 1) / 2 (t - 3989566440250631241736832720104337125491152387032153177635074 t + 1)) infinity ----- \ i ) b(i) t = - 4 ( / ----- i = 0 2 77687315893941101194705928445936884389222409293530391691729 t / + 624402253191220180408517030763314532136003613866383289329002 t + 5) / / ((t - 1) 2 (t - 3989566440250631241736832720104337125491152387032153177635074 t + 1)) infinity ----- \ i ) c(i) t = 29 ( / ----- i = 0 2 7826646900193168440625146688814035630264714506277970296513 t / - 104666587463663690041069692786641817219951062528335029747650 t + 1) / / ((t - 1) 2 (t - 3989566440250631241736832720104337125491152387032153177635074 t + 1)) In Maple notation, these generating functions are 2*(134973255590817393334452185246448590227620809903875134270731*t^2+ 2929831530019758929168505764405175090083008241386782543543938*t-13)/(t-1)/(t^2-\ 3989566440250631241736832720104337125491152387032153177635074*t+1) -4*(77687315893941101194705928445936884389222409293530391691729*t^2+ 624402253191220180408517030763314532136003613866383289329002*t+5)/(t-1)/(t^2-\ 3989566440250631241736832720104337125491152387032153177635074*t+1) 29*(7826646900193168440625146688814035630264714506277970296513*t^2-\ 104666587463663690041069692786641817219951062528335029747650*t+1)/(t-1)/(t^2-\ 3989566440250631241736832720104337125491152387032153177635074*t+1) Then for all i>=0 we have 3 3 3 27 a(i) + 29 b(i) + 29 c(i) = -729 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 470, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (562462931879306805070821340181944871750123765368099 t / ----- i = 0 / + 3208567677719283234139156254959297475996735305095930 t - 29) / ( / 2 (t - 1) (t - 746280566062256564369757600014731282242242822148098 t + 1)) infinity ----- \ i 2 ) b(i) t = - 24 (28944326420206982082611897019631603894003193782129 t / ----- i = 0 / + 25064501802010112546751341419255680577964533582990 t + 1) / ((t - 1) / 2 (t - 746280566062256564369757600014731282242242822148098 t + 1)) infinity ----- \ i 2 ) c(i) t = 33 (17117111998756778542103608040977216316267191524289 t / ----- i = 0 / - 56396259796732847363458690541986150477698265971650 t + 1) / ((t - 1) / 2 (t - 746280566062256564369757600014731282242242822148098 t + 1)) In Maple notation, these generating functions are (562462931879306805070821340181944871750123765368099*t^2+ 3208567677719283234139156254959297475996735305095930*t-29)/(t-1)/(t^2-\ 746280566062256564369757600014731282242242822148098*t+1) -24*(28944326420206982082611897019631603894003193782129*t^2+ 25064501802010112546751341419255680577964533582990*t+1)/(t-1)/(t^2-\ 746280566062256564369757600014731282242242822148098*t+1) 33*(17117111998756778542103608040977216316267191524289*t^2-\ 56396259796732847363458690541986150477698265971650*t+1)/(t-1)/(t^2-\ 746280566062256564369757600014731282242242822148098*t+1) Then for all i>=0 we have 3 3 3 27 a(i) + 31 b(i) + 31 c(i) = -27000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 471, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 31959218330750179 t + 776541130110480250 t - 29 ) a(i) t = ------------------------------------------------ / 2 ----- (t - 1) (t - 528479986796364098 t + 1) i = 0 infinity ----- 2 \ i 36347974910623631 t + 300299881018640474 t + 23 ) b(i) t = - ------------------------------------------------ / 2 ----- (t - 1) (t - 528479986796364098 t + 1) i = 0 infinity ----- 2 \ i 16 (1709965297193759 t - 22750456292772769 t + 2) ) c(i) t = -------------------------------------------------- / 2 ----- (t - 1) (t - 528479986796364098 t + 1) i = 0 In Maple notation, these generating functions are (31959218330750179*t^2+776541130110480250*t-29)/(t-1)/(t^2-528479986796364098*t +1) -(36347974910623631*t^2+300299881018640474*t+23)/(t-1)/(t^2-528479986796364098* t+1) 16*(1709965297193759*t^2-22750456292772769*t+2)/(t-1)/(t^2-528479986796364098*t +1) Then for all i>=0 we have 3 3 3 27 a(i) + 32 b(i) + 32 c(i) = -729 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 472, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = (18214579817858258039829014587305528979223788493549962286\ / ----- i = 0 2 456069646529215648733623379 t + 364295436893034089348398296343664932881\ / 2 450267966668505794375101436466785741362439050 t - 29) / ((t - 1) (t - / 123354077705410933270734547502484711655408334139826385073750526810267863\ 047156402498 t + 1)) infinity ----- \ i ) b(i) t = - 6 (2849758734583772805414383358002635266440780970793535\ / ----- i = 0 2 944038266094186435559421369929 t + 485837915350164411371834132530544098\ / 2 87706352044761263718807959170080823384557648630 t + 1) / ((t - 1) (t - / 123354077705410933270734547502484711655408334139826385073750526810267863\ 047156402498 t + 1)) infinity ----- \ i ) c(i) t = 27 (21660632427022465519403583736287743550132871424545983\ / ----- i = 0 2 0684345120519519962416724809 t - 11646284161959161086882435084264443025\ / 2 311802717702081977983506290356688616634284490 t + 1) / ((t - 1) (t - / 123354077705410933270734547502484711655408334139826385073750526810267863\ 047156402498 t + 1)) In Maple notation, these generating functions are (182145798178582580398290145873055289792237884935499622864560696465292156487336\ 23379*t^2+364295436893034089348398296343664932881450267966668505794375101436466\ 785741362439050*t-29)/(t-1)/(t^2-1233540777054109332707345475024847116554083341\ 39826385073750526810267863047156402498*t+1) -6*(284975873458377280541438335800263526644078097079353594403826609418643555942\ 1369929*t^2+4858379153501644113718341325305440988770635204476126371880795917008\ 0823384557648630*t+1)/(t-1)/(t^2-1233540777054109332707345475024847116554083341\ 39826385073750526810267863047156402498*t+1) 27*(216606324270224655194035837362877435501328714245459830684345120519519962416\ 724809*t^2-11646284161959161086882435084264443025311802717702081977983506290356\ 688616634284490*t+1)/(t-1)/(t^2-12335407770541093327073454750248471165540833413\ 9826385073750526810267863047156402498*t+1) Then for all i>=0 we have 3 3 3 27 a(i) + 34 b(i) + 34 c(i) = -3375 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 473, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 4 (643703273 t + 3642600734 t - 7) ) a(i) t = ----------------------------------- / 2 ----- (t - 1) (t - 3317529602 t + 1) i = 0 infinity ----- 2 \ i 15 (174934321 t + 354755278 t + 1) ) b(i) t = - ----------------------------------- / 2 ----- (t - 1) (t - 3317529602 t + 1) i = 0 infinity ----- 2 \ i 27 (67070961 t - 361342962 t + 1) ) c(i) t = ---------------------------------- / 2 ----- (t - 1) (t - 3317529602 t + 1) i = 0 In Maple notation, these generating functions are 4*(643703273*t^2+3642600734*t-7)/(t-1)/(t^2-3317529602*t+1) -15*(174934321*t^2+354755278*t+1)/(t-1)/(t^2-3317529602*t+1) 27*(67070961*t^2-361342962*t+1)/(t-1)/(t^2-3317529602*t+1) Then for all i>=0 we have 3 3 3 27 a(i) + 38 b(i) + 38 c(i) = -27000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 474, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = ( / ----- i = 0 2 2818657260860904067742114412879299201734052661635803681431259320436777 t + 5069967911451932033677010081206371315908298039281141728263402780508846 t / 2 - 23) / ((t - 1) (t / - 916425895899482390753460332868043132556822053208109755846517099643202 t + 1)) infinity ----- \ i ) b(i) t = - 16 ( / ----- i = 0 2 195612769595645660024755378154519746892985443109744501027179104366936 t - 30604340983586026666902603642346595377380028696390359361734514402937 t / 2 + 1) / ((t - 1) (t / - 916425895899482390753460332868043132556822053208109755846517099643202 t + 1)) infinity ----- \ i ) c(i) t = 5 ( / ----- i = 0 2 499121285967325429030822061514894725979521048177571237622566464554541 t - 1027148257525916255775950939953848810829458374300304490951989152439346 t / 2 + 5) / ((t - 1) (t / - 916425895899482390753460332868043132556822053208109755846517099643202 t + 1)) In Maple notation, these generating functions are (2818657260860904067742114412879299201734052661635803681431259320436777*t^2+ 5069967911451932033677010081206371315908298039281141728263402780508846*t-23)/(t -1)/(t^2-916425895899482390753460332868043132556822053208109755846517099643202* t+1) -16*(195612769595645660024755378154519746892985443109744501027179104366936*t^2-\ 30604340983586026666902603642346595377380028696390359361734514402937*t+1)/(t-1) /(t^2-916425895899482390753460332868043132556822053208109755846517099643202*t+1 ) 5*(499121285967325429030822061514894725979521048177571237622566464554541*t^2-\ 1027148257525916255775950939953848810829458374300304490951989152439346*t+5)/(t-\ 1)/(t^2-916425895899482390753460332868043132556822053208109755846517099643202*t +1) Then for all i>=0 we have 3 3 3 27 a(i) + 40 b(i) + 40 c(i) = -132651 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 475, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 2 (93372199580776502055418498414967 t / ----- i = 0 / + 326027021855452628174254664845046 t - 13) / ((t - 1) / 2 (t - 96309003400254721727235068097602 t + 1)) infinity ----- \ i 2 ) b(i) t = - 3 (55639579555385173805014293812641 t / ----- i = 0 / + 139287669921858162836145540771358 t + 1) / ((t - 1) / 2 (t - 96309003400254721727235068097602 t + 1)) infinity ----- \ i ) c(i) t = 24 ( / ----- i = 0 2 2969548681829027735456484964966 t - 27335454866484444815601464287967 t + 1 / 2 ) / ((t - 1) (t - 96309003400254721727235068097602 t + 1)) / In Maple notation, these generating functions are 2*(93372199580776502055418498414967*t^2+326027021855452628174254664845046*t-13) /(t-1)/(t^2-96309003400254721727235068097602*t+1) -3*(55639579555385173805014293812641*t^2+139287669921858162836145540771358*t+1) /(t-1)/(t^2-96309003400254721727235068097602*t+1) 24*(2969548681829027735456484964966*t^2-27335454866484444815601464287967*t+1)/( t-1)/(t^2-96309003400254721727235068097602*t+1) Then for all i>=0 we have 3 3 3 27 a(i) + 41 b(i) + 41 c(i) = -91125 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 476, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 3 (55784300452211554435821811088846177428447287767 t / ----- i = 0 / + 131005626910813610616096534985394621485541154418 t - 9) / ((t - 1) / 2 (t - 65241066463216746316807652489548583130783857474 t + 1)) infinity ----- \ i 2 ) b(i) t = - (184176540431380600126527083088395350433148726715 t / ----- i = 0 / - 13435503980541490548420649282651773277607611598 t + 19) / ((t - 1) / 2 (t - 65241066463216746316807652489548583130783857474 t + 1)) infinity ----- \ i 2 ) c(i) t = 4 (37486316288471786567045470207332662661877654579 t / ----- i = 0 / - 80171575401181563961572078658768556950762933370 t + 7) / ((t - 1) / 2 (t - 65241066463216746316807652489548583130783857474 t + 1)) In Maple notation, these generating functions are 3*(55784300452211554435821811088846177428447287767*t^2+ 131005626910813610616096534985394621485541154418*t-9)/(t-1)/(t^2-\ 65241066463216746316807652489548583130783857474*t+1) -(184176540431380600126527083088395350433148726715*t^2-\ 13435503980541490548420649282651773277607611598*t+19)/(t-1)/(t^2-\ 65241066463216746316807652489548583130783857474*t+1) 4*(37486316288471786567045470207332662661877654579*t^2-\ 80171575401181563961572078658768556950762933370*t+7)/(t-1)/(t^2-\ 65241066463216746316807652489548583130783857474*t+1) Then for all i>=0 we have 3 3 3 27 a(i) + 44 b(i) + 44 c(i) = -132651 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 477, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 4 (186166199376425 t + 431792442054878 t - 7) ) a(i) t = ---------------------------------------------- / 2 ----- (t - 1) (t - 268510893235202 t + 1) i = 0 infinity ----- 2 \ i 3 (246528672098549 t + 71081355899654 t + 5) ) b(i) t = - --------------------------------------------- / 2 ----- (t - 1) (t - 268510893235202 t + 1) i = 0 infinity ----- 2 \ i 27 (20197245716209 t - 55487248827122 t + 1) ) c(i) t = --------------------------------------------- / 2 ----- (t - 1) (t - 268510893235202 t + 1) i = 0 In Maple notation, these generating functions are 4*(186166199376425*t^2+431792442054878*t-7)/(t-1)/(t^2-268510893235202*t+1) -3*(246528672098549*t^2+71081355899654*t+5)/(t-1)/(t^2-268510893235202*t+1) 27*(20197245716209*t^2-55487248827122*t+1)/(t-1)/(t^2-268510893235202*t+1) Then for all i>=0 we have 3 3 3 27 a(i) + 46 b(i) + 46 c(i) = -157464 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 478, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 16 (60697328639 t + 146145297362 t - 1) ) a(i) t = ---------------------------------------- / 2 ----- (t - 1) (t - 650284185602 t + 1) i = 0 infinity ----- 2 \ i 9 (105623496361 t + 20175527638 t + 1) ) b(i) t = - --------------------------------------- / 2 ----- (t - 1) (t - 650284185602 t + 1) i = 0 infinity ----- 2 \ i 15 (48433216921 t - 123912631322 t + 1) ) c(i) t = ---------------------------------------- / 2 ----- (t - 1) (t - 650284185602 t + 1) i = 0 In Maple notation, these generating functions are 16*(60697328639*t^2+146145297362*t-1)/(t-1)/(t^2-650284185602*t+1) -9*(105623496361*t^2+20175527638*t+1)/(t-1)/(t^2-650284185602*t+1) 15*(48433216921*t^2-123912631322*t+1)/(t-1)/(t^2-650284185602*t+1) Then for all i>=0 we have 3 3 3 27 a(i) + 52 b(i) + 52 c(i) = -27000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 479, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 2 / ----- i = 0 2 (102130533512288493443008658483 t + 251092280783668697788800369626 t - 13) / 2 / ((t - 1) (t - 86967738368322793295710556162 t + 1)) / infinity ----- \ i ) b(i) t = / ----- i = 0 2 3 (66109515618542934870804491717 t + 8816535898781317814730756662 t + 5) - ------------------------------------------------------------------------- 2 (t - 1) (t - 86967738368322793295710556162 t + 1) infinity ----- \ i ) c(i) t = 24 / ----- i = 0 2 (6439929925312715190225406849 t - 15805686364978246775917312898 t + 1) / 2 / ((t - 1) (t - 86967738368322793295710556162 t + 1)) / In Maple notation, these generating functions are 2*(102130533512288493443008658483*t^2+251092280783668697788800369626*t-13)/(t-1 )/(t^2-86967738368322793295710556162*t+1) -3*(66109515618542934870804491717*t^2+8816535898781317814730756662*t+5)/(t-1)/( t^2-86967738368322793295710556162*t+1) 24*(6439929925312715190225406849*t^2-15805686364978246775917312898*t+1)/(t-1)/( t^2-86967738368322793295710556162*t+1) Then for all i>=0 we have 3 3 3 27 a(i) + 56 b(i) + 56 c(i) = -110592 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 480, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = ( / ----- i = 0 2 27916049656715793217285189905003497454654421004202285302371 t / + 70866617073548241503578556038485175018025687581599358603258 t - 29) / / ((t - 1) 2 (t - 9507723956882057427335242776183411046367291637656395502402 t + 1)) infinity ----- \ i ) b(i) t = - 6 ( / ----- i = 0 2 3722982150787472722816570530295165596280686826220386099801 t / + 5009187283931999959690721928797755727271145976944400101798 t + 1) / ( / (t - 1) 2 (t - 9507723956882057427335242776183411046367291637656395502402 t + 1)) infinity ----- \ i ) c(i) t = 24 ( / ----- i = 0 2 494557261810683911684061540308111751341196378364435817101 t / - 2677599620490552082310884655081342082229154579155632367502 t + 1) / ( / (t - 1) 2 (t - 9507723956882057427335242776183411046367291637656395502402 t + 1)) In Maple notation, these generating functions are (27916049656715793217285189905003497454654421004202285302371*t^2+ 70866617073548241503578556038485175018025687581599358603258*t-29)/(t-1)/(t^2-\ 9507723956882057427335242776183411046367291637656395502402*t+1) -6*(3722982150787472722816570530295165596280686826220386099801*t^2+ 5009187283931999959690721928797755727271145976944400101798*t+1)/(t-1)/(t^2-\ 9507723956882057427335242776183411046367291637656395502402*t+1) 24*(494557261810683911684061540308111751341196378364435817101*t^2-\ 2677599620490552082310884655081342082229154579155632367502*t+1)/(t-1)/(t^2-\ 9507723956882057427335242776183411046367291637656395502402*t+1) Then for all i>=0 we have 3 3 3 27 a(i) + 62 b(i) + 62 c(i) = -185193 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 481, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 4 (752760027300546453782873 t + 1030968838859075792975534 t - 7) ----------------------------------------------------------------- 2 (t - 1) (t - 589129480374894462182402 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 2970513063346621229367859 t - 1129491842743509645572678 t + 19 - --------------------------------------------------------------- 2 (t - 1) (t - 589129480374894462182402 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 4 (612342876496176113418007 t - 1072598181646954009366814 t + 7) ----------------------------------------------------------------- 2 (t - 1) (t - 589129480374894462182402 t + 1) In Maple notation, these generating functions are 4*(752760027300546453782873*t^2+1030968838859075792975534*t-7)/(t-1)/(t^2-\ 589129480374894462182402*t+1) -(2970513063346621229367859*t^2-1129491842743509645572678*t+19)/(t-1)/(t^2-\ 589129480374894462182402*t+1) 4*(612342876496176113418007*t^2-1072598181646954009366814*t+7)/(t-1)/(t^2-\ 589129480374894462182402*t+1) Then for all i>=0 we have 3 3 3 27 a(i) + 64 b(i) + 64 c(i) = -373248 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 482, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 4036192025215568381 t + 11684367438598436438 t - 19 ) a(i) t = ---------------------------------------------------- / 2 ----- (t - 1) (t - 2713298141975803202 t + 1) i = 0 infinity ----- 2 \ i 6 (537419081451250441 t + 601751894187445558 t + 1) ) b(i) t = - ---------------------------------------------------- / 2 ----- (t - 1) (t - 2713298141975803202 t + 1) i = 0 infinity ----- 2 \ i 15 (134243792076188809 t - 589912182331667210 t + 1) ) c(i) t = ----------------------------------------------------- / 2 ----- (t - 1) (t - 2713298141975803202 t + 1) i = 0 In Maple notation, these generating functions are (4036192025215568381*t^2+11684367438598436438*t-19)/(t-1)/(t^2-\ 2713298141975803202*t+1) -6*(537419081451250441*t^2+601751894187445558*t+1)/(t-1)/(t^2-\ 2713298141975803202*t+1) 15*(134243792076188809*t^2-589912182331667210*t+1)/(t-1)/(t^2-\ 2713298141975803202*t+1) Then for all i>=0 we have 3 3 3 27 a(i) + 70 b(i) + 70 c(i) = -35937 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 483, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 2 ( / ----- i = 0 2 149009048559146081249540305412197564751772996327658552787 t / + 839418105621298475633357296601445924601594536800994535226 t - 13) / ( / (t - 1) 2 (t - 265168409233950587950913894837395120838574101257004121602 t + 1)) infinity ----- \ i ) b(i) t = - ( / ----- i = 0 2 213911640577741989863761267285930296966295584896969478961 t / + 1007927227120012365993892876889971173005457534368088434638 t + 1) / ( / (t - 1) 2 (t - 265168409233950587950913894837395120838574101257004121602 t + 1)) infinity ----- \ i 2 ) c(i) t = (72745173521708860258933609527006288254089588376029797379 t / ----- i = 0 / - 1294584041219463216116587753702907758225842707641087710998 t + 19) / ( / (t - 1) 2 (t - 265168409233950587950913894837395120838574101257004121602 t + 1)) In Maple notation, these generating functions are 2*(149009048559146081249540305412197564751772996327658552787*t^2+ 839418105621298475633357296601445924601594536800994535226*t-13)/(t-1)/(t^2-\ 265168409233950587950913894837395120838574101257004121602*t+1) -(213911640577741989863761267285930296966295584896969478961*t^2+ 1007927227120012365993892876889971173005457534368088434638*t+1)/(t-1)/(t^2-\ 265168409233950587950913894837395120838574101257004121602*t+1) (72745173521708860258933609527006288254089588376029797379*t^2-\ 1294584041219463216116587753702907758225842707641087710998*t+19)/(t-1)/(t^2-\ 265168409233950587950913894837395120838574101257004121602*t+1) Then for all i>=0 we have 3 3 3 27 a(i) + 76 b(i) + 76 c(i) = -46656 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 484, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (28869708517780821870815097184416355183 t / ----- i = 0 / + 35357884874193786289260785374006684834 t - 17) / ((t - 1) / 2 (t - 7689900112442742995069326300293120002 t + 1)) infinity ----- \ i 2 ) b(i) t = - 6 (3783211703293084775398849789112860801 t / ----- i = 0 / + 472833641958244680991720741866979198 t + 1) / ((t - 1) / 2 (t - 7689900112442742995069326300293120002 t + 1)) infinity ----- \ i 2 ) c(i) t = 15 (988380890084855330690174512292119681 t / ----- i = 0 / - 2690799028185387113246402724684055682 t + 1) / ((t - 1) / 2 (t - 7689900112442742995069326300293120002 t + 1)) In Maple notation, these generating functions are (28869708517780821870815097184416355183*t^2+ 35357884874193786289260785374006684834*t-17)/(t-1)/(t^2-\ 7689900112442742995069326300293120002*t+1) -6*(3783211703293084775398849789112860801*t^2+ 472833641958244680991720741866979198*t+1)/(t-1)/(t^2-\ 7689900112442742995069326300293120002*t+1) 15*(988380890084855330690174512292119681*t^2-\ 2690799028185387113246402724684055682*t+1)/(t-1)/(t^2-\ 7689900112442742995069326300293120002*t+1) Then for all i>=0 we have 3 3 3 27 a(i) + 77 b(i) + 77 c(i) = -110592 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 485, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 2 (97355954430514609589609193839987 t / ----- i = 0 / + 416045761984330950018986023958426 t - 13) / ((t - 1) / 2 (t - 120515317950117931865327889388802 t + 1)) infinity ----- \ i 2 ) b(i) t = - (137822968981751648310360148408081 t / ----- i = 0 / + 472831054947800338889290551175918 t + 1) / ((t - 1) / 2 (t - 120515317950117931865327889388802 t + 1)) infinity ----- \ i 2 ) c(i) t = (50202609994288499679711873952099 t / ----- i = 0 / - 660856633923840486879362573536118 t + 19) / ((t - 1) / 2 (t - 120515317950117931865327889388802 t + 1)) In Maple notation, these generating functions are 2*(97355954430514609589609193839987*t^2+416045761984330950018986023958426*t-13) /(t-1)/(t^2-120515317950117931865327889388802*t+1) -(137822968981751648310360148408081*t^2+472831054947800338889290551175918*t+1)/ (t-1)/(t^2-120515317950117931865327889388802*t+1) (50202609994288499679711873952099*t^2-660856633923840486879362573536118*t+19)/( t-1)/(t^2-120515317950117931865327889388802*t+1) Then for all i>=0 we have 3 3 3 27 a(i) + 80 b(i) + 80 c(i) = -74088 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 486, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 20 (603502826435519 t + 14871216672828482 t - 1) ) a(i) t = ------------------------------------------------- / 2 ----- (t - 1) (t - 307583930787840002 t + 1) i = 0 infinity ----- 2 \ i 15 (751008657776641 t + 3452001576591358 t + 1) ) b(i) t = - ------------------------------------------------ / 2 ----- (t - 1) (t - 307583930787840002 t + 1) i = 0 infinity ----- 2 \ i 18 (534400725960001 t - 4036909254600002 t + 1) ) c(i) t = ------------------------------------------------ / 2 ----- (t - 1) (t - 307583930787840002 t + 1) i = 0 In Maple notation, these generating functions are 20*(603502826435519*t^2+14871216672828482*t-1)/(t-1)/(t^2-307583930787840002*t+ 1) -15*(751008657776641*t^2+3452001576591358*t+1)/(t-1)/(t^2-307583930787840002*t+ 1) 18*(534400725960001*t^2-4036909254600002*t+1)/(t-1)/(t^2-307583930787840002*t+1 ) Then for all i>=0 we have 3 3 3 27 a(i) + 88 b(i) + 88 c(i) = -216 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 487, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 21 (232218228479 t + 1425174784322 t - 1) ) a(i) t = ------------------------------------------ / 2 ----- (t - 1) (t - 9682664443202 t + 1) i = 0 infinity ----- 2 \ i 9 (411186641881 t + 810050314918 t + 1) ) b(i) t = - ---------------------------------------- / 2 ----- (t - 1) (t - 9682664443202 t + 1) i = 0 infinity ----- 2 \ i 15 (177046516585 t - 909788690666 t + 1) ) c(i) t = ----------------------------------------- / 2 ----- (t - 1) (t - 9682664443202 t + 1) i = 0 In Maple notation, these generating functions are 21*(232218228479*t^2+1425174784322*t-1)/(t-1)/(t^2-9682664443202*t+1) -9*(411186641881*t^2+810050314918*t+1)/(t-1)/(t^2-9682664443202*t+1) 15*(177046516585*t^2-909788690666*t+1)/(t-1)/(t^2-9682664443202*t+1) Then for all i>=0 we have 3 3 3 27 a(i) + 98 b(i) + 98 c(i) = -9261 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 488, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (977 t + 460862 t - 15) ) a(i) t = ---------------------------- / 2 ----- (t - 1) (t - 1044482 t + 1) i = 0 infinity ----- 2 \ i 1889 t + 886942 t + 1 ) b(i) t = - ---------------------------- / 2 ----- (t - 1) (t - 1044482 t + 1) i = 0 infinity ----- 2 \ i 125 t - 888986 t + 29 ) c(i) t = ---------------------------- / 2 ----- (t - 1) (t - 1044482 t + 1) i = 0 In Maple notation, these generating functions are 2*(977*t^2+460862*t-15)/(t-1)/(t^2-1044482*t+1) -(1889*t^2+886942*t+1)/(t-1)/(t^2-1044482*t+1) (125*t^2-888986*t+29)/(t-1)/(t^2-1044482*t+1) Then for all i>=0 we have 3 3 3 28 a(i) + 31 b(i) + 31 c(i) = -28 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 489, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 6 (213084168568896989201285657176627009808167 t / ----- i = 0 / + 5586655145212160096252576362374477889794382 t - 5) / ((t - 1) / 2 (t - 22240102535050207422980366412515143931885762 t + 1)) infinity ----- \ i 2 ) b(i) t = - (1351975136936231689479748121965159207239295 t / ----- i = 0 / + 17105978224488670998095573942553397373355694 t + 19) / ((t - 1) / 2 (t - 22240102535050207422980366412515143931885762 t + 1)) infinity ----- \ i 2 ) c(i) t = (887064223695001894858761233579791185839659 t / ----- i = 0 / - 19345017585119904582434083298098347766434698 t + 31) / ((t - 1) / 2 (t - 22240102535050207422980366412515143931885762 t + 1)) In Maple notation, these generating functions are 6*(213084168568896989201285657176627009808167*t^2+ 5586655145212160096252576362374477889794382*t-5)/(t-1)/(t^2-\ 22240102535050207422980366412515143931885762*t+1) -(1351975136936231689479748121965159207239295*t^2+ 17105978224488670998095573942553397373355694*t+19)/(t-1)/(t^2-\ 22240102535050207422980366412515143931885762*t+1) (887064223695001894858761233579791185839659*t^2-\ 19345017585119904582434083298098347766434698*t+31)/(t-1)/(t^2-\ 22240102535050207422980366412515143931885762*t+1) Then for all i>=0 we have 3 3 3 28 a(i) + 33 b(i) + 33 c(i) = -756 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 490, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 3 (152288977574987590157432147332816177810203233 t / ----- i = 0 / + 216986923623020983380624019707563436018246374 t - 7) / ((t - 1) / 2 (t - 119420624220620833916891403370418262301329602 t + 1)) infinity ----- \ i 2 ) b(i) t = - (471157229754452400590996112420263231488986011 t / ----- i = 0 / + 29981068640193865734882927854916393573980378 t + 11) / ((t - 1) / 2 (t - 119420624220620833916891403370418262301329602 t + 1)) infinity ----- \ i 2 ) c(i) t = (330582788916002317368751053343817528894952263 t / ----- i = 0 / - 831721087310648583694630093618997153957918686 t + 23) / ((t - 1) / 2 (t - 119420624220620833916891403370418262301329602 t + 1)) In Maple notation, these generating functions are 3*(152288977574987590157432147332816177810203233*t^2+ 216986923623020983380624019707563436018246374*t-7)/(t-1)/(t^2-\ 119420624220620833916891403370418262301329602*t+1) -(471157229754452400590996112420263231488986011*t^2+ 29981068640193865734882927854916393573980378*t+11)/(t-1)/(t^2-\ 119420624220620833916891403370418262301329602*t+1) (330582788916002317368751053343817528894952263*t^2-\ 831721087310648583694630093618997153957918686*t+23)/(t-1)/(t^2-\ 119420624220620833916891403370418262301329602*t+1) Then for all i>=0 we have 3 3 3 28 a(i) + 39 b(i) + 39 c(i) = -163296 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 491, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (72914781205733513417949114902069476755983977 t / ----- i = 0 / + 598130807818527000493540477698233580808176046 t - 23) / ((t - 1) / 2 (t - 170013971597385835683936720467301082821120002 t + 1)) infinity ----- \ i 2 ) b(i) t = - 6 (10770084723765886237685679489418964288366401 t / ----- i = 0 / + 61607713784243722350610578572247004940433598 t + 1) / ((t - 1) / 2 (t - 170013971597385835683936720467301082821120002 t + 1)) infinity ----- \ i 2 ) c(i) t = 20 (1529680522329317224886891165777401495536961 t / ----- i = 0 / - 23243020074732199801375768584277192264176962 t + 1) / ((t - 1) / 2 (t - 170013971597385835683936720467301082821120002 t + 1)) In Maple notation, these generating functions are (72914781205733513417949114902069476755983977*t^2+ 598130807818527000493540477698233580808176046*t-23)/(t-1)/(t^2-\ 170013971597385835683936720467301082821120002*t+1) -6*(10770084723765886237685679489418964288366401*t^2+ 61607713784243722350610578572247004940433598*t+1)/(t-1)/(t^2-\ 170013971597385835683936720467301082821120002*t+1) 20*(1529680522329317224886891165777401495536961*t^2-\ 23243020074732199801375768584277192264176962*t+1)/(t-1)/(t^2-\ 170013971597385835683936720467301082821120002*t+1) Then for all i>=0 we have 3 3 3 28 a(i) + 45 b(i) + 45 c(i) = -9604 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 492, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (971850807913 t + 1429039780198 t - 15) ) a(i) t = ------------------------------------------ / 2 ----- (t - 1) (t - 280880920322 t + 1) i = 0 infinity ----- 2 \ i 1551363277465 t + 1520884012646 t + 1 ) b(i) t = - -------------------------------------- / 2 ----- (t - 1) (t - 280880920322 t + 1) i = 0 infinity ----- 2 \ i 29 (21687193529 t - 127626755258 t + 1) ) c(i) t = ---------------------------------------- / 2 ----- (t - 1) (t - 280880920322 t + 1) i = 0 In Maple notation, these generating functions are 2*(971850807913*t^2+1429039780198*t-15)/(t-1)/(t^2-280880920322*t+1) -(1551363277465*t^2+1520884012646*t+1)/(t-1)/(t^2-280880920322*t+1) 29*(21687193529*t^2-127626755258*t+1)/(t-1)/(t^2-280880920322*t+1) Then for all i>=0 we have 3 3 3 28 a(i) + 59 b(i) + 59 c(i) = -682892 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 493, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 24 / ----- i = 0 2 (10174222751177434076633086244 t + 274621949740560584337583211057 t - 1) / 2 / ((t - 1) (t - 3786585730030995625112960347202 t + 1)) / infinity ----- \ i ) b(i) t = - 5 / ----- i = 0 2 (34916367362182510510301473045 t + 773744313966470792479923957034 t + 1) / 2 / ((t - 1) (t - 3786585730030995625112960347202 t + 1)) / infinity ----- \ i ) c(i) t = 17 / ----- i = 0 2 (3885693772452152298083594821 t - 241727070633820770824620486022 t + 1) / 2 / ((t - 1) (t - 3786585730030995625112960347202 t + 1)) / In Maple notation, these generating functions are 24*(10174222751177434076633086244*t^2+274621949740560584337583211057*t-1)/(t-1) /(t^2-3786585730030995625112960347202*t+1) -5*(34916367362182510510301473045*t^2+773744313966470792479923957034*t+1)/(t-1) /(t^2-3786585730030995625112960347202*t+1) 17*(3885693772452152298083594821*t^2-241727070633820770824620486022*t+1)/(t-1)/ (t^2-3786585730030995625112960347202*t+1) Then for all i>=0 we have 3 3 3 28 a(i) + 81 b(i) + 81 c(i) = -756 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 494, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 11 (78495532291945005994569017586602015950891033149632972\ / ----- i = 0 2 428549389721689897694799 t + 209572401208435906253938502620009368103181\ / 2 502405366343432505740846730078521202 t - 1) / ((t - 1) (t - 826666510\ / 368115798113407294969413229487080784942477342472298928763367018529602 t + 1 )) infinity ----- \ i ) b(i) t = - 2 (3051723017623032241267194846402997963419076108062340\ / ----- i = 0 2 38861426222576940496981161 t + 4411121016611134943338999976145850229084\ / 2 56004668960450453382022222741908692438 t + 1) / ((t - 1) (t - 8266665\ / 10368115798113407294969413229487080784942477342472298928763367018529602 t + 1)) infinity ----- \ i ) c(i) t = 8 (403159564734343449508357380995490251079851791746433973\ / ----- i = 0 2 52271418688460587801841 t - 2268870573292885245659906086632702299205760\ / 2 83043442019680973479888381189220242 t + 1) / ((t - 1) (t - 8266665103\ / 68115798113407294969413229487080784942477342472298928763367018529602 t + 1) ) In Maple notation, these generating functions are 11*( 78495532291945005994569017586602015950891033149632972428549389721689897694799*t ^2+ 209572401208435906253938502620009368103181502405366343432505740846730078521202* t-1)/(t-1)/(t^2-\ 826666510368115798113407294969413229487080784942477342472298928763367018529602* t+1) -2*( 305172301762303224126719484640299796341907610806234038861426222576940496981161* t^2+ 441112101661113494333899997614585022908456004668960450453382022222741908692438* t+1)/(t-1)/(t^2-\ 826666510368115798113407294969413229487080784942477342472298928763367018529602* t+1) 8*( 40315956473434344950835738099549025107985179174643397352271418688460587801841*t ^2-\ 226887057329288524565990608663270229920576083043442019680973479888381189220242* t+1)/(t-1)/(t^2-\ 826666510368115798113407294969413229487080784942477342472298928763367018529602* t+1) Then for all i>=0 we have 3 3 3 28 a(i) + 93 b(i) + 93 c(i) = -9604 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 495, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (3952051804451012225539518646848848783690891378981 t / ----- i = 0 / + 7045252423870783713551147252368033975267009461038 t - 19) / ((t - 1) / 2 (t - 1563647415078876662975565733694627112003373560002 t + 1)) infinity ----- \ i 2 ) b(i) t = - (3722155976421072581998535140261340121000190338013 t / ----- i = 0 / - 1728921549789189598922863251113360586030182418026 t + 13) / ((t - 1) / 2 (t - 1563647415078876662975565733694627112003373560002 t + 1)) infinity ----- \ i 2 ) c(i) t = (3243119394063374130417987425491782692674021686017 t / ----- i = 0 / - 5236353820695257113493659314639762227644029606034 t + 17) / ((t - 1) / 2 (t - 1563647415078876662975565733694627112003373560002 t + 1)) In Maple notation, these generating functions are (3952051804451012225539518646848848783690891378981*t^2+ 7045252423870783713551147252368033975267009461038*t-19)/(t-1)/(t^2-\ 1563647415078876662975565733694627112003373560002*t+1) -(3722155976421072581998535140261340121000190338013*t^2-\ 1728921549789189598922863251113360586030182418026*t+13)/(t-1)/(t^2-\ 1563647415078876662975565733694627112003373560002*t+1) (3243119394063374130417987425491782692674021686017*t^2-\ 5236353820695257113493659314639762227644029606034*t+17)/(t-1)/(t^2-\ 1563647415078876662975565733694627112003373560002*t+1) Then for all i>=0 we have 3 3 3 28 a(i) + 99 b(i) + 99 c(i) = -76832 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 496, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (1615073766940513508303521502281276938979 t / ----- i = 0 / + 38473896437789177661841609187840148366202 t - 29) / ((t - 1) / 2 (t - 26510559466589039713979040146021768162114 t + 1)) infinity ----- \ i 2 ) b(i) t = - 6 (356048035768706757475102370017399587461 t / ----- i = 0 / + 1824536704417433013838896999506837674358 t + 5) / ((t - 1) / 2 (t - 26510559466589039713979040146021768162114 t + 1)) infinity ----- \ i 2 ) c(i) t = (1782990828094003214909218891480368194365 t / ----- i = 0 / - 14866499269210841842793215108625791765346 t + 37) / ((t - 1) / 2 (t - 26510559466589039713979040146021768162114 t + 1)) In Maple notation, these generating functions are (1615073766940513508303521502281276938979*t^2+ 38473896437789177661841609187840148366202*t-29)/(t-1)/(t^2-\ 26510559466589039713979040146021768162114*t+1) -6*(356048035768706757475102370017399587461*t^2+ 1824536704417433013838896999506837674358*t+5)/(t-1)/(t^2-\ 26510559466589039713979040146021768162114*t+1) (1782990828094003214909218891480368194365*t^2-\ 14866499269210841842793215108625791765346*t+37)/(t-1)/(t^2-\ 26510559466589039713979040146021768162114*t+1) Then for all i>=0 we have 3 3 3 31 a(i) + 32 b(i) + 32 c(i) = -837 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 497, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (360795543935005187 t + 14136453553653651722 t - 13) ) a(i) t = ------------------------------------------------------- / 2 ----- (t - 1) (t - 9621297449150429954 t + 1) i = 0 infinity ----- 2 \ i 694087343359461505 t + 26297787853352151934 t + 1 ) b(i) t = - -------------------------------------------------- / 2 ----- (t - 1) (t - 9621297449150429954 t + 1) i = 0 infinity ----- 2 \ i 116814473063453209 t - 27108689669775066674 t + 25 ) c(i) t = --------------------------------------------------- / 2 ----- (t - 1) (t - 9621297449150429954 t + 1) i = 0 In Maple notation, these generating functions are 2*(360795543935005187*t^2+14136453553653651722*t-13)/(t-1)/(t^2-\ 9621297449150429954*t+1) -(694087343359461505*t^2+26297787853352151934*t+1)/(t-1)/(t^2-\ 9621297449150429954*t+1) (116814473063453209*t^2-27108689669775066674*t+25)/(t-1)/(t^2-\ 9621297449150429954*t+1) Then for all i>=0 we have 3 3 3 31 a(i) + 35 b(i) + 35 c(i) = -1984 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 498, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 146061080899 t + 240525869530 t - 29 ) a(i) t = ------------------------------------- / 2 ----- (t - 1) (t - 27625764098 t + 1) i = 0 infinity ----- 2 \ i 5 (28429491889 t + 25432060750 t + 1) ) b(i) t = - -------------------------------------- / 2 ----- (t - 1) (t - 27625764098 t + 1) i = 0 infinity ----- 2 \ i 32 (2159903719 t - 10575771320 t + 1) ) c(i) t = -------------------------------------- / 2 ----- (t - 1) (t - 27625764098 t + 1) i = 0 In Maple notation, these generating functions are (146061080899*t^2+240525869530*t-29)/(t-1)/(t^2-27625764098*t+1) -5*(28429491889*t^2+25432060750*t+1)/(t-1)/(t^2-27625764098*t+1) 32*(2159903719*t^2-10575771320*t+1)/(t-1)/(t^2-27625764098*t+1) Then for all i>=0 we have 3 3 3 31 a(i) + 38 b(i) + 38 c(i) = -484375 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 499, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (471926648848821013315321421689765611997 t / ----- i = 0 / + 1209620210695647917410196375933766236734 t - 27) / ((t - 1) / 2 (t - 209252815245613354444313063660163427394 t + 1)) infinity ----- \ i 2 ) b(i) t = - (611367751932106968291707496765145878769 t / ----- i = 0 / - 201982364440014198374943686145343241482 t + 25) / ((t - 1) / 2 (t - 209252815245613354444313063660163427394 t + 1)) infinity ----- \ i 2 ) c(i) t = 32 (16704452609839282371610590413570431325 t / ----- i = 0 / - 29497745968967181431509459495439263742 t + 1) / ((t - 1) / 2 (t - 209252815245613354444313063660163427394 t + 1)) In Maple notation, these generating functions are (471926648848821013315321421689765611997*t^2+ 1209620210695647917410196375933766236734*t-27)/(t-1)/(t^2-\ 209252815245613354444313063660163427394*t+1) -(611367751932106968291707496765145878769*t^2-\ 201982364440014198374943686145343241482*t+25)/(t-1)/(t^2-\ 209252815245613354444313063660163427394*t+1) 32*(16704452609839282371610590413570431325*t^2-\ 29497745968967181431509459495439263742*t+1)/(t-1)/(t^2-\ 209252815245613354444313063660163427394*t+1) Then for all i>=0 we have 3 3 3 31 a(i) + 43 b(i) + 43 c(i) = -126976 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 500, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 28 (1001540525121176713838999 t + 36335257738662469981036202 t - 1) -------------------------------------------------------------------- 2 (t - 1) (t - 1024140297560517745488787202 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 7 (4238902351341398967272683 t + 54688925201172460050519314 t + 3) - ------------------------------------------------------------------- 2 (t - 1) (t - 1024140297560517745488787202 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 22194147205151673307577589 t - 434688940072748686432121618 t + 29 ------------------------------------------------------------------ 2 (t - 1) (t - 1024140297560517745488787202 t + 1) In Maple notation, these generating functions are 28*(1001540525121176713838999*t^2+36335257738662469981036202*t-1)/(t-1)/(t^2-\ 1024140297560517745488787202*t+1) -7*(4238902351341398967272683*t^2+54688925201172460050519314*t+3)/(t-1)/(t^2-\ 1024140297560517745488787202*t+1) (22194147205151673307577589*t^2-434688940072748686432121618*t+29)/(t-1)/(t^2-\ 1024140297560517745488787202*t+1) Then for all i>=0 we have 3 3 3 31 a(i) + 45 b(i) + 45 c(i) = -248 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 501, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 6 (875391172521900470813519 t + 907502632430396834548082 t - 1) ---------------------------------------------------------------- 2 (t - 1) (t - 3501859146778815026068802 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 4 (1378938240896619628522441 t - 388047062447036066379242 t + 1) - ----------------------------------------------------------------- 2 (t - 1) (t - 3501859146778815026068802 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 4202666204803627807869487 t - 8166230918601962056442294 t + 7 -------------------------------------------------------------- 2 (t - 1) (t - 3501859146778815026068802 t + 1) In Maple notation, these generating functions are 6*(875391172521900470813519*t^2+907502632430396834548082*t-1)/(t-1)/(t^2-\ 3501859146778815026068802*t+1) -4*(1378938240896619628522441*t^2-388047062447036066379242*t+1)/(t-1)/(t^2-\ 3501859146778815026068802*t+1) (4202666204803627807869487*t^2-8166230918601962056442294*t+7)/(t-1)/(t^2-\ 3501859146778815026068802*t+1) Then for all i>=0 we have 3 3 3 31 a(i) + 48 b(i) + 48 c(i) = -6696 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 502, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (12223861411970985848235275018679700939972841900966377 t / ----- i = 0 / + 745762364940854927806152809449258444861421783087121646 t - 23) / ( / (t - 1) 2 (t - 1486558061832258582898307377598314512810496324230369602 t + 1)) infinity ----- \ i 2 ) b(i) t = - (12390473912945611034602699384345504501359329450090297 t / ----- i = 0 / + 268177562110189951034484233373936077825127039202216886 t + 17) / ( / (t - 1) 2 (t - 1486558061832258582898307377598314512810496324230369602 t + 1)) infinity ----- \ i 2 ) c(i) t = (9334508559952864572543880629675579266366118974848703 t / ----- i = 0 / - 289902544583088426641630813387957161592852487627155926 t + 23) / ( / (t - 1) 2 (t - 1486558061832258582898307377598314512810496324230369602 t + 1)) In Maple notation, these generating functions are (12223861411970985848235275018679700939972841900966377*t^2+ 745762364940854927806152809449258444861421783087121646*t-23)/(t-1)/(t^2-\ 1486558061832258582898307377598314512810496324230369602*t+1) -(12390473912945611034602699384345504501359329450090297*t^2+ 268177562110189951034484233373936077825127039202216886*t+17)/(t-1)/(t^2-\ 1486558061832258582898307377598314512810496324230369602*t+1) (9334508559952864572543880629675579266366118974848703*t^2-\ 289902544583088426641630813387957161592852487627155926*t+23)/(t-1)/(t^2-\ 1486558061832258582898307377598314512810496324230369602*t+1) Then for all i>=0 we have 3 3 3 31 a(i) + 52 b(i) + 52 c(i) = -31 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 503, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 24 (314924358412290319694463655038620746882449514139999 t / ----- i = 0 / + 2721988527418882224622825008155503044858839677684802 t - 1) / ((t - 1) / 2 (t - 24015331604216801067482170017780932826881180600140802 t + 1)) infinity ----- \ i 2 ) b(i) t = - (7755928876439350578132817458176912854446996024473177 t / ----- i = 0 / + 13941861012085544168717977344157543941860806395990806 t + 17) / ( / 2 (t - 1) (t - 24015331604216801067482170017780932826881180600140802 t + 1)) infinity ----- \ i 2 ) c(i) t = (6244291956060357043599391913991533269411238356601183 t / ----- i = 0 / - 27942081844585251790450186716325990065719040777065206 t + 23) / ( / 2 (t - 1) (t - 24015331604216801067482170017780932826881180600140802 t + 1)) In Maple notation, these generating functions are 24*(314924358412290319694463655038620746882449514139999*t^2+ 2721988527418882224622825008155503044858839677684802*t-1)/(t-1)/(t^2-\ 24015331604216801067482170017780932826881180600140802*t+1) -(7755928876439350578132817458176912854446996024473177*t^2+ 13941861012085544168717977344157543941860806395990806*t+17)/(t-1)/(t^2-\ 24015331604216801067482170017780932826881180600140802*t+1) (6244291956060357043599391913991533269411238356601183*t^2-\ 27942081844585251790450186716325990065719040777065206*t+23)/(t-1)/(t^2-\ 24015331604216801067482170017780932826881180600140802*t+1) Then for all i>=0 we have 3 3 3 31 a(i) + 60 b(i) + 60 c(i) = -6696 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 504, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 29 (1059946240981047742634228062261909779930252726599 t / ----- i = 0 / + 6548429205291762100671897317526126917143750361402 t - 1) / ((t - 1) / 2 (t - 41727800051190514088805874168422988828253016936002 t + 1)) infinity ----- \ i 2 ) b(i) t = - (26481407384336909931674446392612329161908375673011 t / ----- i = 0 / + 79838740691299194458981616557068162921037667478978 t + 11) / ((t - 1) / 2 (t - 41727800051190514088805874168422988828253016936002 t + 1)) infinity ----- \ i 2 ) c(i) t = 8 (2029407548523347719109613557176733494489491581153 t / ----- i = 0 / - 15319426057977860767941621425886795004857746975156 t + 3) / ((t - 1) / 2 (t - 41727800051190514088805874168422988828253016936002 t + 1)) In Maple notation, these generating functions are 29*(1059946240981047742634228062261909779930252726599*t^2+ 6548429205291762100671897317526126917143750361402*t-1)/(t-1)/(t^2-\ 41727800051190514088805874168422988828253016936002*t+1) -(26481407384336909931674446392612329161908375673011*t^2+ 79838740691299194458981616557068162921037667478978*t+11)/(t-1)/(t^2-\ 41727800051190514088805874168422988828253016936002*t+1) 8*(2029407548523347719109613557176733494489491581153*t^2-\ 15319426057977860767941621425886795004857746975156*t+3)/(t-1)/(t^2-\ 41727800051190514088805874168422988828253016936002*t+1) Then for all i>=0 we have 3 3 3 31 a(i) + 63 b(i) + 63 c(i) = -31000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 505, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (3904179437 t + 9939473942 t - 3) ) a(i) t = ------------------------------------ / 2 ----- (t - 1) (t - 12444294914 t + 1) i = 0 infinity ----- 2 \ i 6218716609 t + 9274180670 t + 1 ) b(i) t = - -------------------------------- / 2 ----- (t - 1) (t - 12444294914 t + 1) i = 0 infinity ----- 2 \ i 3095373061 t - 18588270346 t + 5 ) c(i) t = --------------------------------- / 2 ----- (t - 1) (t - 12444294914 t + 1) i = 0 In Maple notation, these generating functions are 2*(3904179437*t^2+9939473942*t-3)/(t-1)/(t^2-12444294914*t+1) -(6218716609*t^2+9274180670*t+1)/(t-1)/(t^2-12444294914*t+1) (3095373061*t^2-18588270346*t+5)/(t-1)/(t^2-12444294914*t+1) Then for all i>=0 we have 3 3 3 31 a(i) + 70 b(i) + 70 c(i) = -1984 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 506, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (43673067901394296138028954157895283 t / ----- i = 0 / + 60226701783170245015660416719458970 t - 13) / ((t - 1) / 2 (t - 18888487013710267124171531079204098 t + 1)) infinity ----- \ i 2 ) b(i) t = - 22 (3725542591694675531653062720571937 t / ----- i = 0 / - 3430397585221780191198918579711522 t + 1) / ((t - 1) / 2 (t - 18888487013710267124171531079204098 t + 1)) infinity ----- \ i 2 ) c(i) t = (80142225854724766023949506762670311 t / ----- i = 0 / - 86635415997128463513940677861599486 t + 23) / ((t - 1) / 2 (t - 18888487013710267124171531079204098 t + 1)) In Maple notation, these generating functions are (43673067901394296138028954157895283*t^2+60226701783170245015660416719458970*t-\ 13)/(t-1)/(t^2-18888487013710267124171531079204098*t+1) -22*(3725542591694675531653062720571937*t^2-3430397585221780191198918579711522* t+1)/(t-1)/(t^2-18888487013710267124171531079204098*t+1) (80142225854724766023949506762670311*t^2-86635415997128463513940677861599486*t+ 23)/(t-1)/(t^2-18888487013710267124171531079204098*t+1) Then for all i>=0 we have 3 3 3 31 a(i) + 72 b(i) + 72 c(i) = -41261 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 507, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 6 (794996784456079240903282267 t + 1662229247367215596722805162 t - 5) ----------------------------------------------------------------------- 2 (t - 1) (t - 1038987855899560357388522498 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 3541193380094052616069799521 t + 5276376560467995740170437022 t + 1 - -------------------------------------------------------------------- 2 (t - 1) (t - 1038987855899560357388522498 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 1421201954877841306994380153 t - 10238771895439889663234616722 t + 25 ---------------------------------------------------------------------- 2 (t - 1) (t - 1038987855899560357388522498 t + 1) In Maple notation, these generating functions are 6*(794996784456079240903282267*t^2+1662229247367215596722805162*t-5)/(t-1)/(t^2 -1038987855899560357388522498*t+1) -(3541193380094052616069799521*t^2+5276376560467995740170437022*t+1)/(t-1)/(t^2 -1038987855899560357388522498*t+1) (1421201954877841306994380153*t^2-10238771895439889663234616722*t+25)/(t-1)/(t^ 2-1038987855899560357388522498*t+1) Then for all i>=0 we have 3 3 3 31 a(i) + 81 b(i) + 81 c(i) = -428544 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 508, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 16 ( / ----- i = 0 2 1539424373703679861401862882034616810629133544945955811750987298094 t + 7699760735275925202678202817855643936340421985161401623989411432843 t / 2 - 1) / ((t - 1) (t / - 49265802724251104811903940893137351987839261315278576074783669522498 t + 1)) infinity ----- \ i ) b(i) t = - 2 ( / ----- i = 0 2 20073463741927214974680085363318565629309909894873477485782158712591 t - 15034579900004711453126622902442789676144586526994055037821381475898 t / 2 + 11) / ((t - 1) (t / - 49265802724251104811903940893137351987839261315278576074783669522498 t + 1)) infinity ----- \ i ) c(i) t = ( / ----- i = 0 2 39027346121160844595613361357884682669071359029786259835745417572023 t - 49105113805005851638720286279636234575402005765545104731666972045454 t / 2 + 23) / ((t - 1) (t / - 49265802724251104811903940893137351987839261315278576074783669522498 t + 1)) In Maple notation, these generating functions are 16*(1539424373703679861401862882034616810629133544945955811750987298094*t^2+ 7699760735275925202678202817855643936340421985161401623989411432843*t-1)/(t-1)/ (t^2-49265802724251104811903940893137351987839261315278576074783669522498*t+1) -2*(20073463741927214974680085363318565629309909894873477485782158712591*t^2-\ 15034579900004711453126622902442789676144586526994055037821381475898*t+11)/(t-1 )/(t^2-49265802724251104811903940893137351987839261315278576074783669522498*t+1 ) (39027346121160844595613361357884682669071359029786259835745417572023*t^2-\ 49105113805005851638720286279636234575402005765545104731666972045454*t+23)/(t-1 )/(t^2-49265802724251104811903940893137351987839261315278576074783669522498*t+1 ) Then for all i>=0 we have 3 3 3 31 a(i) + 88 b(i) + 88 c(i) = -6696 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 509, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 21 (59434898057556612997370754134774578250813039 t / ----- i = 0 / + 62246822716735395008054917165963421678318162 t - 1) / ((t - 1) / 2 (t - 237772846322992607815480112099286675981768002 t + 1)) infinity ----- \ i 2 ) b(i) t = - 10 (100584831543987366736392969415121655892294441 t / ----- i = 0 / - 19707553947098328176689168150116103812342122 t + 1) / ((t - 1) / 2 (t - 237772846322992607815480112099286675981768002 t + 1)) infinity ----- \ i 2 ) c(i) t = (738391274180868908875761300544730956794285739 t / ----- i = 0 / - 1547164050149759294472799313194786477593808958 t + 19) / ((t - 1) / 2 (t - 237772846322992607815480112099286675981768002 t + 1)) In Maple notation, these generating functions are 21*(59434898057556612997370754134774578250813039*t^2+ 62246822716735395008054917165963421678318162*t-1)/(t-1)/(t^2-\ 237772846322992607815480112099286675981768002*t+1) -10*(100584831543987366736392969415121655892294441*t^2-\ 19707553947098328176689168150116103812342122*t+1)/(t-1)/(t^2-\ 237772846322992607815480112099286675981768002*t+1) (738391274180868908875761300544730956794285739*t^2-\ 1547164050149759294472799313194786477593808958*t+19)/(t-1)/(t^2-\ 237772846322992607815480112099286675981768002*t+1) Then for all i>=0 we have 3 3 3 31 a(i) + 98 b(i) + 98 c(i) = -287091 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 510, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 22 (2351579 t + 6111734 t - 1) ) a(i) t = ------------------------------- / 2 ----- (t - 1) (t - 28366274 t + 1) i = 0 infinity ----- 2 \ i 18 (3641837 t - 118318 t + 1) ) b(i) t = - ------------------------------ / 2 ----- (t - 1) (t - 28366274 t + 1) i = 0 infinity ----- 2 \ i 26 (2066461 t - 4505822 t + 1) ) c(i) t = ------------------------------- / 2 ----- (t - 1) (t - 28366274 t + 1) i = 0 In Maple notation, these generating functions are 22*(2351579*t^2+6111734*t-1)/(t-1)/(t^2-28366274*t+1) -18*(3641837*t^2-118318*t+1)/(t-1)/(t^2-28366274*t+1) 26*(2066461*t^2-4505822*t+1)/(t-1)/(t^2-28366274*t+1) Then for all i>=0 we have 3 3 3 32 a(i) + 35 b(i) + 35 c(i) = -70304 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 511, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (140758643 t + 603746714 t - 13) ) a(i) t = ----------------------------------- / 2 ----- (t - 1) (t - 268369922 t + 1) i = 0 infinity ----- 2 \ i 22 (16137601 t + 5685886 t + 1) ) b(i) t = - -------------------------------- / 2 ----- (t - 1) (t - 268369922 t + 1) i = 0 infinity ----- 2 \ i 6 (49026437 t - 129045898 t + 5) ) c(i) t = --------------------------------- / 2 ----- (t - 1) (t - 268369922 t + 1) i = 0 In Maple notation, these generating functions are 2*(140758643*t^2+603746714*t-13)/(t-1)/(t^2-268369922*t+1) -22*(16137601*t^2+5685886*t+1)/(t-1)/(t^2-268369922*t+1) 6*(49026437*t^2-129045898*t+5)/(t-1)/(t^2-268369922*t+1) Then for all i>=0 we have 3 3 3 32 a(i) + 37 b(i) + 37 c(i) = -42592 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 512, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (1051379469222905783 t + 2825335360259747750 t - 13) ) a(i) t = ------------------------------------------------------- / 2 ----- (t - 1) (t - 1026445749996828098 t + 1) i = 0 infinity ----- 2 \ i 2 (1315156773442285799 t - 185882826665811250 t + 11) ) b(i) t = - ------------------------------------------------------ / 2 ----- (t - 1) (t - 1026445749996828098 t + 1) i = 0 infinity ----- 2 \ i 30 (74000637329025157 t - 149285567114123462 t + 1) ) c(i) t = ---------------------------------------------------- / 2 ----- (t - 1) (t - 1026445749996828098 t + 1) i = 0 In Maple notation, these generating functions are 2*(1051379469222905783*t^2+2825335360259747750*t-13)/(t-1)/(t^2-\ 1026445749996828098*t+1) -2*(1315156773442285799*t^2-185882826665811250*t+11)/(t-1)/(t^2-\ 1026445749996828098*t+1) 30*(74000637329025157*t^2-149285567114123462*t+1)/(t-1)/(t^2-\ 1026445749996828098*t+1) Then for all i>=0 we have 3 3 3 32 a(i) + 41 b(i) + 41 c(i) = -108000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 513, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 10 (482492677 t + 1992120766 t - 3) ) a(i) t = ------------------------------------ / 2 ----- (t - 1) (t - 3782496002 t + 1) i = 0 infinity ----- 2 \ i 26 (231313321 t + 33153878 t + 1) ) b(i) t = - ---------------------------------- / 2 ----- (t - 1) (t - 3782496002 t + 1) i = 0 infinity ----- 2 \ i 2 (2558242777 t - 5996316394 t + 17) ) c(i) t = ------------------------------------- / 2 ----- (t - 1) (t - 3782496002 t + 1) i = 0 In Maple notation, these generating functions are 10*(482492677*t^2+1992120766*t-3)/(t-1)/(t^2-3782496002*t+1) -26*(231313321*t^2+33153878*t+1)/(t-1)/(t^2-3782496002*t+1) 2*(2558242777*t^2-5996316394*t+17)/(t-1)/(t^2-3782496002*t+1) Then for all i>=0 we have 3 3 3 32 a(i) + 43 b(i) + 43 c(i) = -70304 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 514, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 34768781 t + 92162438 t - 19 ) a(i) t = ----------------------------- / 2 ----- (t - 1) (t - 23020802 t + 1) i = 0 infinity ----- 2 \ i 20 (2432849 t - 1165650 t + 1) ) b(i) t = - ------------------------------- / 2 ----- (t - 1) (t - 23020802 t + 1) i = 0 infinity ----- 2 \ i 8 (5502643 t - 8670646 t + 3) ) c(i) t = ------------------------------ / 2 ----- (t - 1) (t - 23020802 t + 1) i = 0 In Maple notation, these generating functions are (34768781*t^2+92162438*t-19)/(t-1)/(t^2-23020802*t+1) -20*(2432849*t^2-1165650*t+1)/(t-1)/(t^2-23020802*t+1) 8*(5502643*t^2-8670646*t+3)/(t-1)/(t^2-23020802*t+1) Then for all i>=0 we have 3 3 3 32 a(i) + 45 b(i) + 45 c(i) = -42592 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 515, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 6 (21505871587 t + 59272811362 t - 5) ) a(i) t = -------------------------------------- / 2 ----- (t - 1) (t - 56711612162 t + 1) i = 0 infinity ----- 2 \ i 2 (79921904773 t - 18272138642 t + 13) ) b(i) t = - --------------------------------------- / 2 ----- (t - 1) (t - 56711612162 t + 1) i = 0 infinity ----- 2 \ i 34 (4055304889 t - 7681761722 t + 1) ) c(i) t = ------------------------------------- / 2 ----- (t - 1) (t - 56711612162 t + 1) i = 0 In Maple notation, these generating functions are 6*(21505871587*t^2+59272811362*t-5)/(t-1)/(t^2-56711612162*t+1) -2*(79921904773*t^2-18272138642*t+13)/(t-1)/(t^2-56711612162*t+1) 34*(4055304889*t^2-7681761722*t+1)/(t-1)/(t^2-56711612162*t+1) Then for all i>=0 we have 3 3 3 32 a(i) + 47 b(i) + 47 c(i) = -157216 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 516, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 21 (2248491183958628747362559 t + 13799489209494683297648642 t - 1) -------------------------------------------------------------------- 2 (t - 1) (t - 93753990719648296684012802 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 12 (3981382276862014275899761 t + 7843445381472005125687438 t + 1) - ------------------------------------------------------------------- 2 (t - 1) (t - 93753990719648296684012802 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 20 (1714282010929619941331089 t - 8809178605930031582283410 t + 1) ------------------------------------------------------------------- 2 (t - 1) (t - 93753990719648296684012802 t + 1) In Maple notation, these generating functions are 21*(2248491183958628747362559*t^2+13799489209494683297648642*t-1)/(t-1)/(t^2-\ 93753990719648296684012802*t+1) -12*(3981382276862014275899761*t^2+7843445381472005125687438*t+1)/(t-1)/(t^2-\ 93753990719648296684012802*t+1) 20*(1714282010929619941331089*t^2-8809178605930031582283410*t+1)/(t-1)/(t^2-\ 93753990719648296684012802*t+1) Then for all i>=0 we have 3 3 3 32 a(i) + 49 b(i) + 49 c(i) = -10976 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 517, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 30 ( / ----- i = 0 2 2602509335991863130147077982795 t + 2802437620957237009717276467526 t - 1) / 2 / ((t - 1) (t - 11144187487361473707301782206402 t + 1)) / infinity ----- \ i ) b(i) t = - 30 ( / ----- i = 0 2 3179833162333246927125512053853 t - 2083042550261030561684422070814 t + 1) / 2 / ((t - 1) (t - 11144187487361473707301782206402 t + 1)) / infinity ----- \ i 2 ) c(i) t = 2 (42404258107557626354041166266519 t / ----- i = 0 / - 58856117288640871835657516012138 t + 19) / ((t - 1) / 2 (t - 11144187487361473707301782206402 t + 1)) In Maple notation, these generating functions are 30*(2602509335991863130147077982795*t^2+2802437620957237009717276467526*t-1)/(t -1)/(t^2-11144187487361473707301782206402*t+1) -30*(3179833162333246927125512053853*t^2-2083042550261030561684422070814*t+1)/( t-1)/(t^2-11144187487361473707301782206402*t+1) 2*(42404258107557626354041166266519*t^2-58856117288640871835657516012138*t+19)/ (t-1)/(t^2-11144187487361473707301782206402*t+1) Then for all i>=0 we have 3 3 3 32 a(i) + 59 b(i) + 59 c(i) = -780448 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 518, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 2444320876906707782931239 t + 7297934747023571177911970 t - 9 -------------------------------------------------------------- 2 (t - 1) (t - 3769784047848101527308098 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 4 (562692110659695320710009 t + 458421313024975629196550 t + 1) - ---------------------------------------------------------------- 2 (t - 1) (t - 3769784047848101527308098 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 8 (194048881154608096678889 t - 704605592996943571632170 t + 1) ---------------------------------------------------------------- 2 (t - 1) (t - 3769784047848101527308098 t + 1) In Maple notation, these generating functions are (2444320876906707782931239*t^2+7297934747023571177911970*t-9)/(t-1)/(t^2-\ 3769784047848101527308098*t+1) -4*(562692110659695320710009*t^2+458421313024975629196550*t+1)/(t-1)/(t^2-\ 3769784047848101527308098*t+1) 8*(194048881154608096678889*t^2-704605592996943571632170*t+1)/(t-1)/(t^2-\ 3769784047848101527308098*t+1) Then for all i>=0 we have 3 3 3 32 a(i) + 61 b(i) + 61 c(i) = -4000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 519, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 5 (5114919646363 t + 12006061540714 t - 5) ) a(i) t = ------------------------------------------- / 2 ----- (t - 1) (t - 9291462276098 t + 1) i = 0 infinity ----- 2 \ i 6 (3614585865073 t + 4117470154894 t + 1) ) b(i) t = - ------------------------------------------ / 2 ----- (t - 1) (t - 9291462276098 t + 1) i = 0 infinity ----- 2 \ i 2 (5972405551067 t - 29168573610982 t + 11) ) c(i) t = -------------------------------------------- / 2 ----- (t - 1) (t - 9291462276098 t + 1) i = 0 In Maple notation, these generating functions are 5*(5114919646363*t^2+12006061540714*t-5)/(t-1)/(t^2-9291462276098*t+1) -6*(3614585865073*t^2+4117470154894*t+1)/(t-1)/(t^2-9291462276098*t+1) 2*(5972405551067*t^2-29168573610982*t+11)/(t-1)/(t^2-9291462276098*t+1) Then for all i>=0 we have 3 3 3 32 a(i) + 63 b(i) + 63 c(i) = -157216 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 520, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 21 (4536272716924291199 t + 6619667984021040002 t - 1) ) a(i) t = ------------------------------------------------------- / 2 ----- (t - 1) (t - 22402849042891699202 t + 1) i = 0 infinity ----- 2 \ i 4 (19767244537726523041 t + 13229199789013188958 t + 1) ) b(i) t = - -------------------------------------------------------- / 2 ----- (t - 1) (t - 22402849042891699202 t + 1) i = 0 infinity ----- 2 \ i 20 (2048214366437102305 t - 8647503231785044706 t + 1) ) c(i) t = ------------------------------------------------------- / 2 ----- (t - 1) (t - 22402849042891699202 t + 1) i = 0 In Maple notation, these generating functions are 21*(4536272716924291199*t^2+6619667984021040002*t-1)/(t-1)/(t^2-\ 22402849042891699202*t+1) -4*(19767244537726523041*t^2+13229199789013188958*t+1)/(t-1)/(t^2-\ 22402849042891699202*t+1) 20*(2048214366437102305*t^2-8647503231785044706*t+1)/(t-1)/(t^2-\ 22402849042891699202*t+1) Then for all i>=0 we have 3 3 3 32 a(i) + 65 b(i) + 65 c(i) = -219488 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 521, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 13 (425059086688439576488182275857481954351 t / ----- i = 0 / + 852841627648575555158698479311955496850 t - 1) / ((t - 1) / 2 (t - 3651956263638669909550863669217547916098 t + 1)) infinity ----- \ i 2 ) b(i) t = - 8 (664612590969900440636083650154648740553 t / ----- i = 0 / - 102336276661613782711456117880096262026 t + 1) / ((t - 1) / 2 (t - 3651956263638669909550863669217547916098 t + 1)) infinity ----- \ i 2 ) c(i) t = 12 (359351301147362195358201682131170896633 t / ----- i = 0 / - 734202177352886633974620036980872548986 t + 1) / ((t - 1) / 2 (t - 3651956263638669909550863669217547916098 t + 1)) In Maple notation, these generating functions are 13*(425059086688439576488182275857481954351*t^2+ 852841627648575555158698479311955496850*t-1)/(t-1)/(t^2-\ 3651956263638669909550863669217547916098*t+1) -8*(664612590969900440636083650154648740553*t^2-\ 102336276661613782711456117880096262026*t+1)/(t-1)/(t^2-\ 3651956263638669909550863669217547916098*t+1) 12*(359351301147362195358201682131170896633*t^2-\ 734202177352886633974620036980872548986*t+1)/(t-1)/(t^2-\ 3651956263638669909550863669217547916098*t+1) Then for all i>=0 we have 3 3 3 32 a(i) + 77 b(i) + 77 c(i) = -23328 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 522, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 26978955521737 t + 384514759268686 t - 23 ) a(i) t = ------------------------------------------ / 2 ----- (t - 1) (t - 195910354252802 t + 1) i = 0 infinity ----- 2 \ i 10 (2183420571553 t + 15522285084766 t + 1) ) b(i) t = - -------------------------------------------- / 2 ----- (t - 1) (t - 195910354252802 t + 1) i = 0 infinity ----- 2 \ i 18 (768913395361 t - 10605416537762 t + 1) ) c(i) t = ------------------------------------------- / 2 ----- (t - 1) (t - 195910354252802 t + 1) i = 0 In Maple notation, these generating functions are (26978955521737*t^2+384514759268686*t-23)/(t-1)/(t^2-195910354252802*t+1) -10*(2183420571553*t^2+15522285084766*t+1)/(t-1)/(t^2-195910354252802*t+1) 18*(768913395361*t^2-10605416537762*t+1)/(t-1)/(t^2-195910354252802*t+1) Then for all i>=0 we have 3 3 3 32 a(i) + 81 b(i) + 81 c(i) = -2048 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 523, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (13905647639305520987865780904069804787970095030383 t / ----- i = 0 / + 230779763749872573408087728646390735764346302851234 t - 17) / ((t - 1) / 2 (t - 141895192906053050174822354853463418493809052652802 t + 1)) infinity ----- \ i 2 ) b(i) t = - 4 (2492854341073276452162660857643193738745297097841 t / ----- i = 0 / + 31025695164293585793858367847899346062941880694158 t + 1) / ((t - 1) / 2 (t - 141895192906053050174822354853463418493809052652802 t + 1)) infinity ----- \ i 2 ) c(i) t = 12 (367429859047574784458694255745404419982762531601 t / ----- i = 0 / - 11540279694169862199799037157592917687211821795602 t + 1) / ((t - 1) / 2 (t - 141895192906053050174822354853463418493809052652802 t + 1)) In Maple notation, these generating functions are (13905647639305520987865780904069804787970095030383*t^2+ 230779763749872573408087728646390735764346302851234*t-17)/(t-1)/(t^2-\ 141895192906053050174822354853463418493809052652802*t+1) -4*(2492854341073276452162660857643193738745297097841*t^2+ 31025695164293585793858367847899346062941880694158*t+1)/(t-1)/(t^2-\ 141895192906053050174822354853463418493809052652802*t+1) 12*(367429859047574784458694255745404419982762531601*t^2-\ 11540279694169862199799037157592917687211821795602*t+1)/(t-1)/(t^2-\ 141895192906053050174822354853463418493809052652802*t+1) Then for all i>=0 we have 3 3 3 32 a(i) + 95 b(i) + 95 c(i) = -864 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 524, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 239971518935251 t + 4334413049295178 t - 29 ) a(i) t = -------------------------------------------- / 2 ----- (t - 1) (t - 2213213018860802 t + 1) i = 0 infinity ----- 2 \ i 2 (94092294851287 t + 719679622947106 t + 7) ) b(i) t = - --------------------------------------------- / 2 ----- (t - 1) (t - 2213213018860802 t + 1) i = 0 infinity ----- 2 \ i 22 (5909530728241 t - 79888795982642 t + 1) ) c(i) t = -------------------------------------------- / 2 ----- (t - 1) (t - 2213213018860802 t + 1) i = 0 In Maple notation, these generating functions are (239971518935251*t^2+4334413049295178*t-29)/(t-1)/(t^2-2213213018860802*t+1) -2*(94092294851287*t^2+719679622947106*t+7)/(t-1)/(t^2-2213213018860802*t+1) 22*(5909530728241*t^2-79888795982642*t+1)/(t-1)/(t^2-2213213018860802*t+1) Then for all i>=0 we have 3 3 3 32 a(i) + 99 b(i) + 99 c(i) = -2048 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 525, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 26 (94139853874532026846950485384682328426970510472640073\ / ----- i = 0 2 40442285499013390854808784777439 t + 1065517023903227423907731856791746\ / 6749577673249044956809583252418439524209034566915362 t - 1) / ((t - 1) ( / 2 t - 3769680813539364521934858249666608293244790062469712974165380844835\ 4380606537877145602 t + 1)) infinity ----- \ i ) b(i) t = - 9 (2578059929170960201096631024348765768892174874023232\ / ----- i = 0 2 3661498512276891599509741256164881 t + 63116027982232436241008839804299\ / 99269257487326993284056101124593001342529359426523118 t + 1) / ((t - 1) ( / 2 t - 3769680813539364521934858249666608293244790062469712974165380844835\ 4380606537877145602 t + 1)) infinity ----- \ i ) c(i) t = (13788553975085439125174630680670659077332522818945083954\ / ----- i = 0 2 9063755501890487039583457709549 t - 42671535856025000196735105482196550\ / 3396938352794481309007460487330926965391489601901578 t + 29) / ((t - 1) ( / 2 t - 3769680813539364521934858249666608293244790062469712974165380844835\ 4380606537877145602 t + 1)) In Maple notation, these generating functions are 26*(941398538745320268469504853846823284269705104726400734044228549901339085480\ 8784777439*t^2+1065517023903227423907731856791746674957767324904495680958325241\ 8439524209034566915362*t-1)/(t-1)/(t^2-3769680813539364521934858249666608293244\ 7900624697129741653808448354380606537877145602*t+1) -9*(257805992917096020109663102434876576889217487402323236614985122768915995097\ 41256164881*t^2+631160279822324362410088398042999926925748732699328405610112459\ 3001342529359426523118*t+1)/(t-1)/(t^2-3769680813539364521934858249666608293244\ 7900624697129741653808448354380606537877145602*t+1) (137885539750854391251746306806706590773325228189450839549063755501890487039583\ 457709549*t^2-42671535856025000196735105482196550339693835279448130900746048733\ 0926965391489601901578*t+29)/(t-1)/(t^2-376968081353936452193485824966660829324\ 47900624697129741653808448354380606537877145602*t+1) Then for all i>=0 we have 3 3 3 35 a(i) + 52 b(i) + 52 c(i) = -615160 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 526, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 30 (5749276947750989505265799948798745599 t / ----- i = 0 / + 232745236652384416323050926083844454402 t - 1) / ((t - 1) / 2 (t - 6863514748069043356655303825727696000002 t + 1)) infinity ----- \ i 2 ) b(i) t = - 17 (9280005848996710415699194771313052001 t / ----- i = 0 / + 182648899519956863924007693394446947998 t + 1) / ((t - 1) / 2 (t - 6863514748069043356655303825727696000002 t + 1)) infinity ----- \ i 2 ) c(i) t = 9 (11540069783086505606113270732481516003 t / ----- i = 0 / - 374072446591109923803337392823361516006 t + 3) / ((t - 1) / 2 (t - 6863514748069043356655303825727696000002 t + 1)) In Maple notation, these generating functions are 30*(5749276947750989505265799948798745599*t^2+ 232745236652384416323050926083844454402*t-1)/(t-1)/(t^2-\ 6863514748069043356655303825727696000002*t+1) -17*(9280005848996710415699194771313052001*t^2+ 182648899519956863924007693394446947998*t+1)/(t-1)/(t^2-\ 6863514748069043356655303825727696000002*t+1) 9*(11540069783086505606113270732481516003*t^2-\ 374072446591109923803337392823361516006*t+3)/(t-1)/(t^2-\ 6863514748069043356655303825727696000002*t+1) Then for all i>=0 we have 3 3 3 35 a(i) + 64 b(i) + 64 c(i) = -280 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 527, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 21 (13590423527712200995824743372439779170978574918685712\ / ----- i = 0 2 08571592005678473531970295 t + 1734160922648598954626009382305496691453\ / 2 0074026784971045640582995288279930180234 t - 1) / ((t - 1) (t - 98395\ / 150196820218964383578830182196481644977427617478946831609524954209441580\ 098 t + 1)) infinity ----- \ i ) b(i) t = - (217199005588839548696080490361407812707630989778145774\ / ----- i = 0 2 32504013681435959031769929 t + 2513591506481501330051128966159067243831\ / 2 41463927026883961786356365793785233408310 t + 1) / ((t - 1) (t - 9839\ / 515019682021896438357883018219648164497742761747894683160952495420944158\ 0098 t + 1)) infinity ----- \ i ) c(i) t = 16 (36652540270123252340494886051839826487217259829257791\ / ----- i = 0 2 6614715017615860489090614 t - 17433966103140863015575007963771367368241\ / 2 207779845169253757863145567719505664255 t + 1) / ((t - 1) (t - 983951\ / 501968202189643835788301821964816449774276174789468316095249542094415800\ 98 t + 1)) In Maple notation, these generating functions are 21*(135904235277122009958247433724397791709785749186857120857159200567847353197\ 0295*t^2+1734160922648598954626009382305496691453007402678497104564058299528827\ 9930180234*t-1)/(t-1)/(t^2-9839515019682021896438357883018219648164497742761747\ 8946831609524954209441580098*t+1) -(21719900558883954869608049036140781270763098977814577432504013681435959031769\ 929*t^2+25135915064815013300511289661590672438314146392702688396178635636579378\ 5233408310*t+1)/(t-1)/(t^2-9839515019682021896438357883018219648164497742761747\ 8946831609524954209441580098*t+1) 16*( 366525402701232523404948860518398264872172598292577916614715017615860489090614* t^2-174339661031408630155750079637713673682412077798451692537578631455677195056\ 64255*t+1)/(t-1)/(t^2-983951501968202189643835788301821964816449774276174789468\ 31609524954209441580098*t+1) Then for all i>=0 we have 3 3 3 35 a(i) + 81 b(i) + 81 c(i) = -7560 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 528, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 20 (179466409235576264506201595 t + 4543458631505459319774766886 t - 1) ------------------------------------------------------------------------ 2 (t - 1) (t - 92397887795300190051988929602 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 12 (261594983666546543869621831 t + 2382858391384789552622776168 t + 1) - ------------------------------------------------------------------------ 2 (t - 1) (t - 92397887795300190051988929602 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 2323383398382302778680000177 t - 34056823898998335936588776194 t + 17 ---------------------------------------------------------------------- 2 (t - 1) (t - 92397887795300190051988929602 t + 1) In Maple notation, these generating functions are 20*(179466409235576264506201595*t^2+4543458631505459319774766886*t-1)/(t-1)/(t^ 2-92397887795300190051988929602*t+1) -12*(261594983666546543869621831*t^2+2382858391384789552622776168*t+1)/(t-1)/(t ^2-92397887795300190051988929602*t+1) (2323383398382302778680000177*t^2-34056823898998335936588776194*t+17)/(t-1)/(t^ 2-92397887795300190051988929602*t+1) Then for all i>=0 we have 3 3 3 35 a(i) + 88 b(i) + 88 c(i) = -280 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 529, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = ( / ----- i = 0 2 15426277522690135333133950535799247059707832302432543502623983 t + 350590208833934130874218763135374555215947142200498222551936034 t - 17) / / ((t - 1) ( / 2 t - 184284451289736903906351924177536600587882072239271975656480002 t + 1) ) infinity ----- \ i ) b(i) t = - 2 ( / ----- i = 0 2 6378497233612523542996378208795871697205004985471240133046001 t + 131451978800262723145964894721771668908690173697640763820553998 t + 1) / / ((t - 1) ( / 2 t - 184284451289736903906351924177536600587882072239271975656480002 t + 1) ) infinity ----- \ i ) c(i) t = 2 ( / ----- i = 0 2 1750613976805482943056193048056097579292655294741477082258807 t - 139581090010680729632017465978623638185187833977853481035858814 t + 7) / / ((t - 1) ( / 2 t - 184284451289736903906351924177536600587882072239271975656480002 t + 1) ) In Maple notation, these generating functions are (15426277522690135333133950535799247059707832302432543502623983*t^2+ 350590208833934130874218763135374555215947142200498222551936034*t-17)/(t-1)/(t^ 2-184284451289736903906351924177536600587882072239271975656480002*t+1) -2*(6378497233612523542996378208795871697205004985471240133046001*t^2+ 131451978800262723145964894721771668908690173697640763820553998*t+1)/(t-1)/(t^2 -184284451289736903906351924177536600587882072239271975656480002*t+1) 2*(1750613976805482943056193048056097579292655294741477082258807*t^2-\ 139581090010680729632017465978623638185187833977853481035858814*t+7)/(t-1)/(t^2 -184284451289736903906351924177536600587882072239271975656480002*t+1) Then for all i>=0 we have 3 3 3 36 a(i) + 65 b(i) + 65 c(i) = -972 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 530, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 18 (165541257359165800714079056540394495999 t / ----- i = 0 / + 995857106915109221153456791729317504002 t - 1) / ((t - 1) / 2 (t - 6863514748069043356655303825727696000002 t + 1)) infinity ----- \ i 2 ) b(i) t = - (3385648413118883734741806719887541052013 t / ----- i = 0 / + 4375133967550017581951626808015082947974 t + 13) / ((t - 1) / 2 (t - 6863514748069043356655303825727696000002 t + 1)) infinity ----- \ i 2 ) c(i) t = (2640712755002637631528450965455765820019 t / ----- i = 0 / - 10401495135671538948221884493358389820038 t + 19) / ((t - 1) / 2 (t - 6863514748069043356655303825727696000002 t + 1)) In Maple notation, these generating functions are 18*(165541257359165800714079056540394495999*t^2+ 995857106915109221153456791729317504002*t-1)/(t-1)/(t^2-\ 6863514748069043356655303825727696000002*t+1) -(3385648413118883734741806719887541052013*t^2+ 4375133967550017581951626808015082947974*t+13)/(t-1)/(t^2-\ 6863514748069043356655303825727696000002*t+1) (2640712755002637631528450965455765820019*t^2-\ 10401495135671538948221884493358389820038*t+19)/(t-1)/(t^2-\ 6863514748069043356655303825727696000002*t+1) Then for all i>=0 we have 3 3 3 37 a(i) + 48 b(i) + 48 c(i) = -7992 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 531, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 21 (227423851818059168093667856253759 t / ----- i = 0 / + 3764047763328882771197580392917442 t - 1) / ((t - 1) / 2 (t - 55598377346339726608915468036435202 t + 1)) infinity ----- \ i 2 ) b(i) t = - 21 (284955810332177490572827923220081 t / ----- i = 0 / + 709552268862683463998055478930318 t + 1) / ((t - 1) / 2 (t - 55598377346339726608915468036435202 t + 1)) infinity ----- \ i 2 ) c(i) t = 5 (1037617707122504042740309778146709 t / ----- i = 0 / - 5214551639740920051938020067178394 t + 5) / ((t - 1) / 2 (t - 55598377346339726608915468036435202 t + 1)) In Maple notation, these generating functions are 21*(227423851818059168093667856253759*t^2+3764047763328882771197580392917442*t-\ 1)/(t-1)/(t^2-55598377346339726608915468036435202*t+1) -21*(284955810332177490572827923220081*t^2+709552268862683463998055478930318*t+ 1)/(t-1)/(t^2-55598377346339726608915468036435202*t+1) 5*(1037617707122504042740309778146709*t^2-5214551639740920051938020067178394*t+ 5)/(t-1)/(t^2-55598377346339726608915468036435202*t+1) Then for all i>=0 we have 3 3 3 37 a(i) + 54 b(i) + 54 c(i) = -999 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 532, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = (83510458261401956053912207639199493887559746014579586566\ / ----- i = 0 2 753174977025877468945309347 t + 196119616727674633380553407911599017837\ / 2 508689881994451142390950648909977487612349818 t - 29) / ((t - 1) (t - / 280851167019596574541166338762810732300287075354637679795210257178887539\ 91269983234 t + 1)) infinity ----- \ i ) b(i) t = - (774106553232524314043628092240531796680227548502265534\ / ----- i = 0 2 92668710702134170677143580555 t + 5813056006446591543941746730930330418\ / 2 1246224994837718060671891675502859454637642858 t + 11) / ((t - 1) (t - / 280851167019596574541166338762810732300287075354637679795210257178887539\ 91269983234 t + 1)) infinity ----- \ i ) c(i) t = 3 (165246119675950375732418022258844494573898353929000082\ / ----- i = 0 2 12361439681041848284720603593 t - 6170501709683448652116856107033661074\ / 2 0479495341254765396808307140254191661981011410 t + 9) / ((t - 1) (t - / 280851167019596574541166338762810732300287075354637679795210257178887539\ 91269983234 t + 1)) In Maple notation, these generating functions are (835104582614019560539122076391994938875597460145795865667531749770258774689453\ 09347*t^2+196119616727674633380553407911599017837508689881994451142390950648909\ 977487612349818*t-29)/(t-1)/(t^2-2808511670195965745411663387628107323002870753\ 5463767979521025717888753991269983234*t+1) -(77410655323252431404362809224053179668022754850226553492668710702134170677143\ 580555*t^2+58130560064465915439417467309303304181246224994837718060671891675502\ 859454637642858*t+11)/(t-1)/(t^2-2808511670195965745411663387628107323002870753\ 5463767979521025717888753991269983234*t+1) 3*(1652461196759503757324180222588444945738983539290000821236143968104184828472\ 0603593*t^2-6170501709683448652116856107033661074047949534125476539680830714025\ 4191661981011410*t+9)/(t-1)/(t^2-2808511670195965745411663387628107323002870753\ 5463767979521025717888753991269983234*t+1) Then for all i>=0 we have 3 3 3 37 a(i) + 63 b(i) + 63 c(i) = -253783 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 533, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 9819080804070282934425581 t + 26397810411496717633689638 t - 19 ---------------------------------------------------------------- 2 (t - 1) (t - 6515965349719198316236802 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 10529087828757315153419533 t + 260163177490503051252454 t + 13 - --------------------------------------------------------------- 2 (t - 1) (t - 6515965349719198316236802 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 8565271667943258566534419 t - 19354522674191076771206438 t + 19 ---------------------------------------------------------------- 2 (t - 1) (t - 6515965349719198316236802 t + 1) In Maple notation, these generating functions are (9819080804070282934425581*t^2+26397810411496717633689638*t-19)/(t-1)/(t^2-\ 6515965349719198316236802*t+1) -(10529087828757315153419533*t^2+260163177490503051252454*t+13)/(t-1)/(t^2-\ 6515965349719198316236802*t+1) (8565271667943258566534419*t^2-19354522674191076771206438*t+19)/(t-1)/(t^2-\ 6515965349719198316236802*t+1) Then for all i>=0 we have 3 3 3 37 a(i) + 65 b(i) + 65 c(i) = -49247 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 534, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = (34091649079288177931503241743584567478030002186202347392\ / ----- i = 0 2 3699780186133034625840273610217 t + 91697143732285907408789439705738169\ / 71883423879658043056761903690919010895671424295655982 t - 23) / ((t - 1) / 2 (t - 516255365559505504770201537884054812800890061910556050260729692241\ 8560255116658172006402 t + 1)) infinity ----- \ i ) b(i) t = - (283942504755201175517760293285797539296639602849270207\ / ----- i = 0 2 295376872859058259255609811505541 t + 644636683430812434921686115562647\ / 7430504628870683700418456640806699625312649416096071286 t + 5) / ((t - 1) / 2 (t - 516255365559505504770201537884054812800890061910556050260729692241\ 8560255116658172006402 t + 1)) infinity ----- \ i ) c(i) t = (10037208663595714050197360697418832979955497569279602902\ / ----- i = 0 2 8769298912678932918618894946195 t - 68306814256992826652365950558864632\ / 99600823449225766654780786978471362504823644802523046 t + 19) / ((t - 1) / 2 (t - 516255365559505504770201537884054812800890061910556050260729692241\ 8560255116658172006402 t + 1)) In Maple notation, these generating functions are (340916490792881779315032417435845674780300021862023473923699780186133034625840\ 273610217*t^2+91697143732285907408789439705738169718834238796580430567619036909\ 19010895671424295655982*t-23)/(t-1)/(t^2-51625536555950550477020153788405481280\ 08900619105560502607296922418560255116658172006402*t+1) -(28394250475520117551776029328579753929663960284927020729537687285905825925560\ 9811505541*t^2+6446366834308124349216861155626477430504628870683700418456640806\ 699625312649416096071286*t+5)/(t-1)/(t^2-51625536555950550477020153788405481280\ 08900619105560502607296922418560255116658172006402*t+1) (100372086635957140501973606974188329799554975692796029028769298912678932918618\ 894946195*t^2-68306814256992826652365950558864632996008234492257666547807869784\ 71362504823644802523046*t+19)/(t-1)/(t^2-51625536555950550477020153788405481280\ 08900619105560502607296922418560255116658172006402*t+1) Then for all i>=0 we have 3 3 3 37 a(i) + 67 b(i) + 67 c(i) = -999 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 535, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 2 (22745109520813790075534748894140257715509 t / ----- i = 0 / + 78135407835592213660608685955555870009302 t - 11) / ((t - 1) / 2 (t - 30585972834133114763133390476443592640002 t + 1)) infinity ----- \ i 2 ) b(i) t = - 5 (7813717409728998995154119402615144279281 t / ----- i = 0 / + 15607158831781975666076544643955488484878 t + 1) / ((t - 1) / 2 (t - 30585972834133114763133390476443592640002 t + 1)) infinity ----- \ i 2 ) c(i) t = (20337320384445403148859627335548450336579 t / ----- i = 0 / - 137441701592000276455012947568401614157398 t + 19) / ((t - 1) / 2 (t - 30585972834133114763133390476443592640002 t + 1)) In Maple notation, these generating functions are 2*(22745109520813790075534748894140257715509*t^2+ 78135407835592213660608685955555870009302*t-11)/(t-1)/(t^2-\ 30585972834133114763133390476443592640002*t+1) -5*(7813717409728998995154119402615144279281*t^2+ 15607158831781975666076544643955488484878*t+1)/(t-1)/(t^2-\ 30585972834133114763133390476443592640002*t+1) (20337320384445403148859627335548450336579*t^2-\ 137441701592000276455012947568401614157398*t+19)/(t-1)/(t^2-\ 30585972834133114763133390476443592640002*t+1) Then for all i>=0 we have 3 3 3 37 a(i) + 68 b(i) + 68 c(i) = -63936 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 536, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 2 ( / ----- i = 0 1265661069443004629325580471002920092199633757818171998543669151961240709 2 t + 6676777658140402606910218295957271676968517717739411776942942938719821702 t / 2 - 11) / ((t - 1) (t - / 3944507125918665252973608580452202862938891371829607188946826408264249602 t + 1)) infinity ----- \ i ) b(i) t = - 17 ( / ----- i = 0 2 163193561803123937900828038917316392450750374917196837021591105994789201 t + 69360038503327711590644834501987560695560575699234658383055146198721198 t / 2 + 1) / ((t - 1) (t - / 3944507125918665252973608580452202862938891371829607188946826408264249602 t + 1)) infinity ----- \ i ) c(i) t = 2 ( / ----- i = 0 1176201763752719367269441585630035987131439227159811114926246208962168091 2 t - 3152907366357558387946961009694119588875082307399478825865739352607006502 t / 2 + 11) / ((t - 1) (t - / 3944507125918665252973608580452202862938891371829607188946826408264249602 t + 1)) In Maple notation, these generating functions are 2*(1265661069443004629325580471002920092199633757818171998543669151961240709*t^ 2+6676777658140402606910218295957271676968517717739411776942942938719821702*t-\ 11)/(t-1)/(t^2-\ 3944507125918665252973608580452202862938891371829607188946826408264249602*t+1) -17*(163193561803123937900828038917316392450750374917196837021591105994789201*t ^2+69360038503327711590644834501987560695560575699234658383055146198721198*t+1) /(t-1)/(t^2-\ 3944507125918665252973608580452202862938891371829607188946826408264249602*t+1) 2*(1176201763752719367269441585630035987131439227159811114926246208962168091*t^ 2-3152907366357558387946961009694119588875082307399478825865739352607006502*t+ 11)/(t-1)/(t^2-\ 3944507125918665252973608580452202862938891371829607188946826408264249602*t+1) Then for all i>=0 we have 3 3 3 37 a(i) + 72 b(i) + 72 c(i) = -18944 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 537, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 1655369050245745273 t + 6739926295402641310 t - 23 ) a(i) t = --------------------------------------------------- / 2 ----- (t - 1) (t - 1677091641362032898 t + 1) i = 0 infinity ----- 2 \ i 5 (454419562970797781 t - 225635819704718554 t + 5) ) b(i) t = - ---------------------------------------------------- / 2 ----- (t - 1) (t - 1677091641362032898 t + 1) i = 0 infinity ----- 2 \ i 4 (530402429844275743 t - 816382108926874790 t + 7) ) c(i) t = ---------------------------------------------------- / 2 ----- (t - 1) (t - 1677091641362032898 t + 1) i = 0 In Maple notation, these generating functions are (1655369050245745273*t^2+6739926295402641310*t-23)/(t-1)/(t^2-\ 1677091641362032898*t+1) -5*(454419562970797781*t^2-225635819704718554*t+5)/(t-1)/(t^2-\ 1677091641362032898*t+1) 4*(530402429844275743*t^2-816382108926874790*t+7)/(t-1)/(t^2-\ 1677091641362032898*t+1) Then for all i>=0 we have 3 3 3 37 a(i) + 77 b(i) + 77 c(i) = -37000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 538, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = ( / ----- i = 0 2 5935970463008639000650305061090103486916516350792176260432224999 t + 177379489018162191389395156509857310258295392641222186428504551794 t / 2 - 25) / ((t - 1) (t / - 98957902905764784546838700494051258747415278305423682513496844098 t + 1) ) infinity ----- \ i ) b(i) t = - ( / ----- i = 0 2 4545413616180242298182715785839137618108089825151327669141360797 t + 115501878433436053709457674977436159878756346151920024888215466462 t + 5 / 2 ) / ((t - 1) (t / - 98957902905764784546838700494051258747415278305423682513496844098 t + 1) ) infinity ----- \ i ) c(i) t = 19 ( / ----- i = 0 2 83022546561890673571450697647057151297359560513433659943434121 t - 6401301075489064147657787053608914914290224611938241689278003978 t + 1) / 2 / ((t - 1) (t / - 98957902905764784546838700494051258747415278305423682513496844098 t + 1) ) In Maple notation, these generating functions are (5935970463008639000650305061090103486916516350792176260432224999*t^2+ 177379489018162191389395156509857310258295392641222186428504551794*t-25)/(t-1)/ (t^2-98957902905764784546838700494051258747415278305423682513496844098*t+1) -(4545413616180242298182715785839137618108089825151327669141360797*t^2+ 115501878433436053709457674977436159878756346151920024888215466462*t+5)/(t-1)/( t^2-98957902905764784546838700494051258747415278305423682513496844098*t+1) 19*(83022546561890673571450697647057151297359560513433659943434121*t^2-\ 6401301075489064147657787053608914914290224611938241689278003978*t+1)/(t-1)/(t^ 2-98957902905764784546838700494051258747415278305423682513496844098*t+1) Then for all i>=0 we have 3 3 3 37 a(i) + 86 b(i) + 86 c(i) = -999 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 539, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 4 ( / ----- i = 0 2 14102917726865523204860986018187459558320951673054111953418287 t + 379512749866087940393476682679672072461596067674343577432374902 t - 5) / / ((t - 1) ( / 2 t - 1487331225399640225471614746838314010956188543581163905359031362 t + 1 )) infinity ----- \ i ) b(i) t = - 9 ( / ----- i = 0 2 5117090540419964770516631871640099626142879662914949722730209 t + 75296737359069075980382512520472180803009433851891691635422942 t + 1) / / ((t - 1) ( / 2 t - 1487331225399640225471614746838314010956188543581163905359031362 t + 1 )) infinity ----- \ i ) c(i) t = 8 ( / ----- i = 0 2 3513080855971127129694235807247107149677860945520709718209485 t - 93978637242896297974455773248373422632474213649678181246131783 t + 2) / / ((t - 1) ( / 2 t - 1487331225399640225471614746838314010956188543581163905359031362 t + 1 )) In Maple notation, these generating functions are 4*(14102917726865523204860986018187459558320951673054111953418287*t^2+ 379512749866087940393476682679672072461596067674343577432374902*t-5)/(t-1)/(t^2 -1487331225399640225471614746838314010956188543581163905359031362*t+1) -9*(5117090540419964770516631871640099626142879662914949722730209*t^2+ 75296737359069075980382512520472180803009433851891691635422942*t+1)/(t-1)/(t^2-\ 1487331225399640225471614746838314010956188543581163905359031362*t+1) 8*(3513080855971127129694235807247107149677860945520709718209485*t^2-\ 93978637242896297974455773248373422632474213649678181246131783*t+2)/(t-1)/(t^2-\ 1487331225399640225471614746838314010956188543581163905359031362*t+1) Then for all i>=0 we have 3 3 3 37 a(i) + 88 b(i) + 88 c(i) = -296 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 540, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 19 ( / ----- i = 0 2 1255287556087578739466256100624183018976421870049612608497936087999 t + 3450566133219665360755219187753662123592046350103547895242978267202 t / 2 - 1) / ((t - 1) (t / - 15885560620738450610129704438875166834601513403194977090058013619202 t + 1)) infinity ----- \ i ) b(i) t = - 9 ( / ----- i = 0 2 2332195944105344048283221634389581606002606881428145520362610324641 t + 1092001664181182178215747726994939227749102017324416670252220523358 t / 2 + 1) / ((t - 1) (t / - 15885560620738450610129704438875166834601513403194977090058013619202 t + 1)) infinity ----- \ i ) c(i) t = 16 ( / ----- i = 0 2 964040958226656084765537041462855608535082810977085028265998516561 t - 2890152112887827087171207307241648577520419066525401260486840868562 t / 2 + 1) / ((t - 1) (t / - 15885560620738450610129704438875166834601513403194977090058013619202 t + 1)) In Maple notation, these generating functions are 19*(1255287556087578739466256100624183018976421870049612608497936087999*t^2+ 3450566133219665360755219187753662123592046350103547895242978267202*t-1)/(t-1)/ (t^2-15885560620738450610129704438875166834601513403194977090058013619202*t+1) -9*(2332195944105344048283221634389581606002606881428145520362610324641*t^2+ 1092001664181182178215747726994939227749102017324416670252220523358*t+1)/(t-1)/ (t^2-15885560620738450610129704438875166834601513403194977090058013619202*t+1) 16*(964040958226656084765537041462855608535082810977085028265998516561*t^2-\ 2890152112887827087171207307241648577520419066525401260486840868562*t+1)/(t-1)/ (t^2-15885560620738450610129704438875166834601513403194977090058013619202*t+1) Then for all i>=0 we have 3 3 3 37 a(i) + 90 b(i) + 90 c(i) = -49247 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 541, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 1068128730930753395879 t + 21505796943278318309234 t - 25 ) a(i) t = ---------------------------------------------------------- / 2 ----- (t - 1) (t - 14968640464926213252098 t + 1) i = 0 infinity ----- 2 \ i 21 (53130589452949195201 t + 176392699897349143102 t + 1) ) b(i) t = - ---------------------------------------------------------- / 2 ----- (t - 1) (t - 14968640464926213252098 t + 1) i = 0 infinity ----- 2 \ i 963152559807539756953 t - 5783141636163804861362 t + 25 ) c(i) t = -------------------------------------------------------- / 2 ----- (t - 1) (t - 14968640464926213252098 t + 1) i = 0 In Maple notation, these generating functions are (1068128730930753395879*t^2+21505796943278318309234*t-25)/(t-1)/(t^2-\ 14968640464926213252098*t+1) -21*(53130589452949195201*t^2+176392699897349143102*t+1)/(t-1)/(t^2-\ 14968640464926213252098*t+1) (963152559807539756953*t^2-5783141636163804861362*t+25)/(t-1)/(t^2-\ 14968640464926213252098*t+1) Then for all i>=0 we have 3 3 3 37 a(i) + 91 b(i) + 91 c(i) = -999 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 542, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 14 (2844818446900417521374794697820547962725580191 t / ----- i = 0 / + 3115946153375462890510485722218079602862638178 t - 1) / ((t - 1) / 2 (t - 11385730135358423258657277206815356024157271042 t + 1)) infinity ----- \ i 2 ) b(i) t = - (31917567037926139455283767915870093170113400693 t / ----- i = 0 / + 2775422433342467885801347337837874009377578118 t + 5) / ((t - 1) / 2 (t - 11385730135358423258657277206815356024157271042 t + 1)) infinity ----- \ i 2 ) c(i) t = (20538293250324469369784589124587901319211079933 t / ----- i = 0 / - 55231282721593076710869704378295868498702058762 t + 13) / ((t - 1) / 2 (t - 11385730135358423258657277206815356024157271042 t + 1)) In Maple notation, these generating functions are 14*(2844818446900417521374794697820547962725580191*t^2+ 3115946153375462890510485722218079602862638178*t-1)/(t-1)/(t^2-\ 11385730135358423258657277206815356024157271042*t+1) -(31917567037926139455283767915870093170113400693*t^2+ 2775422433342467885801347337837874009377578118*t+5)/(t-1)/(t^2-\ 11385730135358423258657277206815356024157271042*t+1) (20538293250324469369784589124587901319211079933*t^2-\ 55231282721593076710869704378295868498702058762*t+13)/(t-1)/(t^2-\ 11385730135358423258657277206815356024157271042*t+1) Then for all i>=0 we have 3 3 3 37 a(i) + 98 b(i) + 98 c(i) = -101528 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 543, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 90669367 t + 5969435194 t - 17 ) a(i) t = ------------------------------- / 2 ----- (t - 1) (t - 9720776834 t + 1) i = 0 infinity ----- 2 \ i 91055609 t + 5169238178 t + 5 ) b(i) t = - ------------------------------- / 2 ----- (t - 1) (t - 9720776834 t + 1) i = 0 infinity ----- 2 \ i 30609365 t - 5290903174 t + 17 ) c(i) t = ------------------------------- / 2 ----- (t - 1) (t - 9720776834 t + 1) i = 0 In Maple notation, these generating functions are (90669367*t^2+5969435194*t-17)/(t-1)/(t^2-9720776834*t+1) -(91055609*t^2+5169238178*t+5)/(t-1)/(t^2-9720776834*t+1) (30609365*t^2-5290903174*t+17)/(t-1)/(t^2-9720776834*t+1) Then for all i>=0 we have 3 3 3 38 a(i) + 39 b(i) + 39 c(i) = -38 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 544, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 9 (138297019450759596666552228852885216593160820830917469\ / ----- i = 0 2 965871387320378122352797 t + 385172413206905364466504445320106858097004\ / 2 930663156716615833043937858981767206 t - 3) / ((t - 1) (t - 499346417\ / 327818649560104753704190596593844749121075376140151231661083320520002 t + 1 )) infinity ----- \ i ) b(i) t = - 6 (2082475146282968530588220089053116169084729586906431\ / ----- i = 0 2 42469965790837449700606201 t + 3417572348921990508044817777833620836876\ / 2 45895413729735597447159977656565473798 t + 1) / ((t - 1) (t - 4993464\ / 17327818649560104753704190596593844749121075376140151231661083320520002 t + 1)) infinity ----- \ i ) c(i) t = 4 (156787125060340733338361755898471556695403514601182559\ / ----- i = 0 2 993343375520749163262407 t - 981794249341084589133317435931482107589581\ / 2 795757741877094462801743408562382414 t + 7) / ((t - 1) (t - 499346417\ / 327818649560104753704190596593844749121075376140151231661083320520002 t + 1 )) In Maple notation, these generating functions are 9*( 138297019450759596666552228852885216593160820830917469965871387320378122352797* t^2+ 385172413206905364466504445320106858097004930663156716615833043937858981767206* t-3)/(t-1)/(t^2-\ 499346417327818649560104753704190596593844749121075376140151231661083320520002* t+1) -6*( 208247514628296853058822008905311616908472958690643142469965790837449700606201* t^2+ 341757234892199050804481777783362083687645895413729735597447159977656565473798* t+1)/(t-1)/(t^2-\ 499346417327818649560104753704190596593844749121075376140151231661083320520002* t+1) 4*( 156787125060340733338361755898471556695403514601182559993343375520749163262407* t^2-\ 981794249341084589133317435931482107589581795757741877094462801743408562382414* t+7)/(t-1)/(t^2-\ 499346417327818649560104753704190596593844749121075376140151231661083320520002* t+1) Then for all i>=0 we have 3 3 3 38 a(i) + 43 b(i) + 43 c(i) = -186694 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 545, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 12 (35016523878373754570383100436673288799490434687473421\ / ----- i = 0 2 35005336977490868239764141155834299497 t + 3995318431355572260294314981\ / 250226397027406097138281801183297173003554746255541267407846411 t - 2) / / 2 ((t - 1) (t - 763421634277134458980782026589695945278303415280073516368\ 2652725331551844275169841081566914 t + 1)) infinity ----- \ i ) b(i) t = - 3 (1535448267021576917801973187952161703404324290044422\ / ----- i = 0 2 3871377061796539996724901722806996252259 t - 21711182730640380630197349\ 65319594940680900615796629743768889048881050783384306722127652768 t + 5) / 2 / ((t - 1) (t - 7634216342771344589807820265896959452783034152800735\ / 163682652725331551844275169841081566914 t + 1)) infinity ----- \ i ) c(i) t = (33546903305186050581241406546307164892950169068363448663\ / ----- i = 0 2 473810661567524977250365991623601135 t - 730969964966412439262413972889\ / 13231173037195922306231046298328904544362801802614246229399652 t + 29) / / 2 ((t - 1) (t - 763421634277134458980782026589695945278303415280073516368\ 2652725331551844275169841081566914 t + 1)) In Maple notation, these generating functions are 12*(350165238783737545703831004366732887994904346874734213500533697749086823976\ 4141155834299497*t^2+3995318431355572260294314981250226397027406097138281801183\ 297173003554746255541267407846411*t-2)/(t-1)/(t^2-76342163427713445898078202658\ 96959452783034152800735163682652725331551844275169841081566914*t+1) -3*(153544826702157691780197318795216170340432429004442238713770617965399967249\ 01722806996252259*t^2-217111827306403806301973496531959494068090061579662974376\ 8889048881050783384306722127652768*t+5)/(t-1)/(t^2-7634216342771344589807820265\ 896959452783034152800735163682652725331551844275169841081566914*t+1) (335469033051860505812414065463071648929501690683634486634738106615675249772503\ 65991623601135*t^2-730969964966412439262413972889132311730371959223062310462983\ 28904544362801802614246229399652*t+29)/(t-1)/(t^2-76342163427713445898078202658\ 96959452783034152800735163682652725331551844275169841081566914*t+1) Then for all i>=0 we have 3 3 3 38 a(i) + 47 b(i) + 47 c(i) = -462346 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 546, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (747311496831988717915452045758632076941 t / ----- i = 0 / + 44700351553298818617890642531474001233478 t - 19) / ((t - 1) / 2 (t - 80726670897264310747162423701111846382402 t + 1)) infinity ----- \ i 2 ) b(i) t = - 8 (89153870979413623496507969413159414861 t / ----- i = 0 / + 3853794064876683816596258226785105575538 t + 1) / ((t - 1) / 2 (t - 80726670897264310747162423701111846382402 t + 1)) infinity ----- \ i 2 ) c(i) t = 2 (169787609709657314507168866212979640209 t / ----- i = 0 / - 15941579353134047074878233651006039601818 t + 9) / ((t - 1) / 2 (t - 80726670897264310747162423701111846382402 t + 1)) In Maple notation, these generating functions are (747311496831988717915452045758632076941*t^2+ 44700351553298818617890642531474001233478*t-19)/(t-1)/(t^2-\ 80726670897264310747162423701111846382402*t+1) -8*(89153870979413623496507969413159414861*t^2+ 3853794064876683816596258226785105575538*t+1)/(t-1)/(t^2-\ 80726670897264310747162423701111846382402*t+1) 2*(169787609709657314507168866212979640209*t^2-\ 15941579353134047074878233651006039601818*t+9)/(t-1)/(t^2-\ 80726670897264310747162423701111846382402*t+1) Then for all i>=0 we have 3 3 3 38 a(i) + 49 b(i) + 49 c(i) = -38 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 547, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = ( / ----- i = 0 2 8927907910211859993894304956097037597315661743261967436815337 t + 20606995911984056687964257857763604776806582705220999592023086 t - 23) / / ((t - 1) / 2 (t - 2999456072684101272095897305021458009505952021278275469824002 t + 1)) infinity ----- \ i ) b(i) t = - 2 ( / ----- i = 0 2 3919647305003986125446288662129019073848399418889029782564161 t + 6146059827224218662989813462774159493117029182387676469416638 t + 1) / / ((t - 1) / 2 (t - 2999456072684101272095897305021458009505952021278275469824002 t + 1)) infinity ----- \ i ) c(i) t = 2 ( / ----- i = 0 2 1687670327451021126972712423104759674519483983073537923360331 t - 11753377459679225915408814548007938241484912584350244175341142 t + 11) / / ((t - 1) / 2 (t - 2999456072684101272095897305021458009505952021278275469824002 t + 1)) In Maple notation, these generating functions are (8927907910211859993894304956097037597315661743261967436815337*t^2+ 20606995911984056687964257857763604776806582705220999592023086*t-23)/(t-1)/(t^2 -2999456072684101272095897305021458009505952021278275469824002*t+1) -2*(3919647305003986125446288662129019073848399418889029782564161*t^2+ 6146059827224218662989813462774159493117029182387676469416638*t+1)/(t-1)/(t^2-\ 2999456072684101272095897305021458009505952021278275469824002*t+1) 2*(1687670327451021126972712423104759674519483983073537923360331*t^2-\ 11753377459679225915408814548007938241484912584350244175341142*t+11)/(t-1)/(t^2 -2999456072684101272095897305021458009505952021278275469824002*t+1) Then for all i>=0 we have 3 3 3 38 a(i) + 61 b(i) + 61 c(i) = -186694 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 548, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (21598637344630544836300793984924054745583 t / ----- i = 0 / + 131373035845713849136095676585981544774434 t - 17) / ((t - 1) / 2 (t - 36678544673078171241965421829776610080002 t + 1)) infinity ----- \ i 2 ) b(i) t = - 2 (8867731078639898224786901110441945647601 t / ----- i = 0 / + 42347454659096550858482401811975788112398 t + 1) / ((t - 1) / 2 (t - 36678544673078171241965421829776610080002 t + 1)) infinity ----- \ i 2 ) c(i) t = 14 (495438820354608859387386087744418851601 t / ----- i = 0 / - 7811893925745530156997286505232666531602 t + 1) / ((t - 1) / 2 (t - 36678544673078171241965421829776610080002 t + 1)) In Maple notation, these generating functions are (21598637344630544836300793984924054745583*t^2+ 131373035845713849136095676585981544774434*t-17)/(t-1)/(t^2-\ 36678544673078171241965421829776610080002*t+1) -2*(8867731078639898224786901110441945647601*t^2+ 42347454659096550858482401811975788112398*t+1)/(t-1)/(t^2-\ 36678544673078171241965421829776610080002*t+1) 14*(495438820354608859387386087744418851601*t^2-\ 7811893925745530156997286505232666531602*t+1)/(t-1)/(t^2-\ 36678544673078171241965421829776610080002*t+1) Then for all i>=0 we have 3 3 3 38 a(i) + 73 b(i) + 73 c(i) = -13034 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 549, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 27 ( / ----- i = 0 2 9623331652084997662513123862111 t + 57121247983229836748289267381218 t - 1 / 2 ) / ((t - 1) (t - 397518044669248252734713423460674 t + 1)) / infinity ----- \ i 2 ) b(i) t = - 4 (68256155391657118780159612193477 t / ----- i = 0 / + 43822304028691522963675499779766 t + 5) / ((t - 1) / 2 (t - 397518044669248252734713423460674 t + 1)) infinity ----- \ i 2 ) c(i) t = 2 (114859814566122992819664695697205 t / ----- i = 0 / - 339016733406820276307334919643714 t + 13) / ((t - 1) / 2 (t - 397518044669248252734713423460674 t + 1)) In Maple notation, these generating functions are 27*(9623331652084997662513123862111*t^2+57121247983229836748289267381218*t-1)/( t-1)/(t^2-397518044669248252734713423460674*t+1) -4*(68256155391657118780159612193477*t^2+43822304028691522963675499779766*t+5)/ (t-1)/(t^2-397518044669248252734713423460674*t+1) 2*(114859814566122992819664695697205*t^2-339016733406820276307334919643714*t+13 )/(t-1)/(t^2-397518044669248252734713423460674*t+1) Then for all i>=0 we have 3 3 3 38 a(i) + 81 b(i) + 81 c(i) = -27702 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 550, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 11205199 t + 12637762 t - 17 ) a(i) t = ----------------------------- / 2 ----- (t - 1) (t - 2979074 t + 1) i = 0 infinity ----- 2 \ i 16619159 t - 14452270 t + 23 ) b(i) t = - ----------------------------- / 2 ----- (t - 1) (t - 2979074 t + 1) i = 0 infinity ----- 2 \ i 15940057 t - 18106994 t + 25 ) c(i) t = ----------------------------- / 2 ----- (t - 1) (t - 2979074 t + 1) i = 0 In Maple notation, these generating functions are (11205199*t^2+12637762*t-17)/(t-1)/(t^2-2979074*t+1) -(16619159*t^2-14452270*t+23)/(t-1)/(t^2-2979074*t+1) (15940057*t^2-18106994*t+25)/(t-1)/(t^2-2979074*t+1) Then for all i>=0 we have 3 3 3 38 a(i) + 99 b(i) + 99 c(i) = -155648 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 551, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 16 (17260304773709212214 t + 23247505959425805059 t - 1) ) a(i) t = --------------------------------------------------------- / 2 ----- (t - 1) (t - 90692536148237255234 t + 1) i = 0 infinity ----- 2 \ i 11 (29806320928122630529 t - 3654223503502423490 t + 1) ) b(i) t = - -------------------------------------------------------- / 2 ----- (t - 1) (t - 90692536148237255234 t + 1) i = 0 infinity ----- 2 \ i 4 (61255016823886179299 t - 133173284741591748664 t + 5) ) c(i) t = --------------------------------------------------------- / 2 ----- (t - 1) (t - 90692536148237255234 t + 1) i = 0 In Maple notation, these generating functions are 16*(17260304773709212214*t^2+23247505959425805059*t-1)/(t-1)/(t^2-\ 90692536148237255234*t+1) -11*(29806320928122630529*t^2-3654223503502423490*t+1)/(t-1)/(t^2-\ 90692536148237255234*t+1) 4*(61255016823886179299*t^2-133173284741591748664*t+5)/(t-1)/(t^2-\ 90692536148237255234*t+1) Then for all i>=0 we have 3 3 3 39 a(i) + 40 b(i) + 40 c(i) = -107016 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 552, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (23292796867187 t + 41129606716826 t - 13) ) a(i) t = --------------------------------------------- / 2 ----- (t - 1) (t - 10266243993602 t + 1) i = 0 infinity ----- 2 \ i 3 (14222926552961 t + 15335588032638 t + 1) ) b(i) t = - -------------------------------------------- / 2 ----- (t - 1) (t - 10266243993602 t + 1) i = 0 infinity ----- 2 \ i 3 (6458660930569 t - 36017175516178 t + 9) ) c(i) t = ------------------------------------------- / 2 ----- (t - 1) (t - 10266243993602 t + 1) i = 0 In Maple notation, these generating functions are 2*(23292796867187*t^2+41129606716826*t-13)/(t-1)/(t^2-10266243993602*t+1) -3*(14222926552961*t^2+15335588032638*t+1)/(t-1)/(t^2-10266243993602*t+1) 3*(6458660930569*t^2-36017175516178*t+9)/(t-1)/(t^2-10266243993602*t+1) Then for all i>=0 we have 3 3 3 39 a(i) + 56 b(i) + 56 c(i) = -415272 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 553, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 29 (370743707843363941417800931512959 t / ----- i = 0 / + 803730778671193053967265876874434 t - 1) / ((t - 1) / 2 (t - 3576901811265664625663892770091842 t + 1)) infinity ----- \ i 2 ) b(i) t = - 6 (2431914043357328660662499662293149 t / ----- i = 0 / - 1369196392076393444477281953178786 t + 5) / ((t - 1) / 2 (t - 3576901811265664625663892770091842 t + 1)) infinity ----- \ i 2 ) c(i) t = 36 (367987175533660491009318599917345 t / ----- i = 0 / - 545106784080483027040188218103074 t + 1) / ((t - 1) / 2 (t - 3576901811265664625663892770091842 t + 1)) In Maple notation, these generating functions are 29*(370743707843363941417800931512959*t^2+803730778671193053967265876874434*t-1 )/(t-1)/(t^2-3576901811265664625663892770091842*t+1) -6*(2431914043357328660662499662293149*t^2-1369196392076393444477281953178786*t +5)/(t-1)/(t^2-3576901811265664625663892770091842*t+1) 36*(367987175533660491009318599917345*t^2-545106784080483027040188218103074*t+1 )/(t-1)/(t^2-3576901811265664625663892770091842*t+1) Then for all i>=0 we have 3 3 3 39 a(i) + 62 b(i) + 62 c(i) = -267501 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 554, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 11 (513122019406239125195363825099188822684067327 t / ----- i = 0 / + 19156642029991526986767996691787735763549497858 t - 1) / ((t - 1) / 2 (t - 363918815091579873309304925093234590410630746114 t + 1)) infinity ----- \ i 2 ) b(i) t = - 3 (1552019067610539218764582140035104829319369025 t / ----- i = 0 / + 46805165901969069159643908758214125242280627902 t + 1) / ((t - 1) / 2 (t - 363918815091579873309304925093234590410630746114 t + 1)) infinity ----- \ i 2 ) c(i) t = 9 (203765121788589163079916153562197329243970753 t / ----- i = 0 / - 16322826778315125289216079786311940686443969730 t + 1) / ((t - 1) / 2 (t - 363918815091579873309304925093234590410630746114 t + 1)) In Maple notation, these generating functions are 11*(513122019406239125195363825099188822684067327*t^2+ 19156642029991526986767996691787735763549497858*t-1)/(t-1)/(t^2-\ 363918815091579873309304925093234590410630746114*t+1) -3*(1552019067610539218764582140035104829319369025*t^2+ 46805165901969069159643908758214125242280627902*t+1)/(t-1)/(t^2-\ 363918815091579873309304925093234590410630746114*t+1) 9*(203765121788589163079916153562197329243970753*t^2-\ 16322826778315125289216079786311940686443969730*t+1)/(t-1)/(t^2-\ 363918815091579873309304925093234590410630746114*t+1) Then for all i>=0 we have 3 3 3 39 a(i) + 74 b(i) + 74 c(i) = -39 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 555, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 464390899 t + 2063991082 t - 29 ) a(i) t = -------------------------------- / 2 ----- (t - 1) (t - 416731394 t + 1) i = 0 infinity ----- 2 \ i 24 (24661153 t + 13596766 t + 1) ) b(i) t = - --------------------------------- / 2 ----- (t - 1) (t - 416731394 t + 1) i = 0 infinity ----- 2 \ i 2 (239300801 t - 698395858 t + 17) ) c(i) t = ----------------------------------- / 2 ----- (t - 1) (t - 416731394 t + 1) i = 0 In Maple notation, these generating functions are (464390899*t^2+2063991082*t-29)/(t-1)/(t^2-416731394*t+1) -24*(24661153*t^2+13596766*t+1)/(t-1)/(t^2-416731394*t+1) 2*(239300801*t^2-698395858*t+17)/(t-1)/(t^2-416731394*t+1) Then for all i>=0 we have 3 3 3 40 a(i) + 41 b(i) + 41 c(i) = -69120 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 556, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 21277725612764100013 t + 55083310803042389614 t - 27 ) a(i) t = ----------------------------------------------------- / 2 ----- (t - 1) (t - 9448986023047771202 t + 1) i = 0 infinity ----- 2 \ i 22 (1227363427216355881 t - 24695283534691882 t + 1) ) b(i) t = - ----------------------------------------------------- / 2 ----- (t - 1) (t - 9448986023047771202 t + 1) i = 0 infinity ----- 2 \ i 32 (689177722397552081 t - 1516012071178696082 t + 1) ) c(i) t = ------------------------------------------------------ / 2 ----- (t - 1) (t - 9448986023047771202 t + 1) i = 0 In Maple notation, these generating functions are (21277725612764100013*t^2+55083310803042389614*t-27)/(t-1)/(t^2-\ 9448986023047771202*t+1) -22*(1227363427216355881*t^2-24695283534691882*t+1)/(t-1)/(t^2-\ 9448986023047771202*t+1) 32*(689177722397552081*t^2-1516012071178696082*t+1)/(t-1)/(t^2-\ 9448986023047771202*t+1) Then for all i>=0 we have 3 3 3 40 a(i) + 43 b(i) + 43 c(i) = -163840 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 557, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 8 (11567356400695612613585926 t + 12794415472533402949294453 t - 3) -------------------------------------------------------------------- 2 (t - 1) (t - 16804280067327861599548994 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 2 (58273974540081386832244747 t - 27348835362721123997528278 t + 11) - --------------------------------------------------------------------- 2 (t - 1) (t - 16804280067327861599548994 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 16 (6053676987648937969606559 t - 9919319384818970823946121 t + 2) ------------------------------------------------------------------- 2 (t - 1) (t - 16804280067327861599548994 t + 1) In Maple notation, these generating functions are 8*(11567356400695612613585926*t^2+12794415472533402949294453*t-3)/(t-1)/(t^2-\ 16804280067327861599548994*t+1) -2*(58273974540081386832244747*t^2-27348835362721123997528278*t+11)/(t-1)/(t^2-\ 16804280067327861599548994*t+1) 16*(6053676987648937969606559*t^2-9919319384818970823946121*t+2)/(t-1)/(t^2-\ 16804280067327861599548994*t+1) Then for all i>=0 we have 3 3 3 40 a(i) + 47 b(i) + 47 c(i) = -486680 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 558, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 28 ( / ----- i = 0 2 9070616058960723135951292238928798660714903858442771750325932843799 t + 15765322887550130144846331949187334811544100578496803864589696436202 t / 2 - 1) / ((t - 1) (t / - 65714649311132508411507614694555470625169257234015384245639614080002 t + 1)) infinity ----- \ i ) b(i) t = - 24 ( / ----- i = 0 2 13283406840341321376066064888679944530305504010576523358786138031001 t - 4459368039167483924943644030461761620646462657903771716030740431002 t / 2 + 1) / ((t - 1) (t / - 65714649311132508411507614694555470625169257234015384245639614080002 t + 1)) infinity ----- \ i ) c(i) t = 2 ( / ----- i = 0 2 133484836201350933267217657981505623904480608531367503875930991104017 t - 239373301815436982680686708280123818820389104763440523588995762304034 t / 2 + 17) / ((t - 1) (t / - 65714649311132508411507614694555470625169257234015384245639614080002 t + 1)) In Maple notation, these generating functions are 28*(9070616058960723135951292238928798660714903858442771750325932843799*t^2+ 15765322887550130144846331949187334811544100578496803864589696436202*t-1)/(t-1) /(t^2-65714649311132508411507614694555470625169257234015384245639614080002*t+1) -24*(13283406840341321376066064888679944530305504010576523358786138031001*t^2-\ 4459368039167483924943644030461761620646462657903771716030740431002*t+1)/(t-1)/ (t^2-65714649311132508411507614694555470625169257234015384245639614080002*t+1) 2*(133484836201350933267217657981505623904480608531367503875930991104017*t^2-\ 239373301815436982680686708280123818820389104763440523588995762304034*t+17)/(t-\ 1)/(t^2-65714649311132508411507614694555470625169257234015384245639614080002*t+ 1) Then for all i>=0 we have 3 3 3 40 a(i) + 49 b(i) + 49 c(i) = -370440 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 559, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 2 (10400318695606109446367759715640075481696531989 t / ----- i = 0 / + 204127998991732626391461038608233919623588127222 t - 11) / ((t - 1) / 2 (t - 266074023310154679231357456960045092327378227202 t + 1)) infinity ----- \ i 2 ) b(i) t = - 10 (1934765206983839058236946310427822300047948801 t / ----- i = 0 / + 22610808899118991129157653040129843043806131198 t + 1) / ((t - 1) / 2 (t - 266074023310154679231357456960045092327378227202 t + 1)) infinity ----- \ i 2 ) c(i) t = 20 (551369855667675151263762766588308130756113121 t / ----- i = 0 / - 12824156908719090244961062441867140802683153122 t + 1) / ((t - 1) / 2 (t - 266074023310154679231357456960045092327378227202 t + 1)) In Maple notation, these generating functions are 2*(10400318695606109446367759715640075481696531989*t^2+ 204127998991732626391461038608233919623588127222*t-11)/(t-1)/(t^2-\ 266074023310154679231357456960045092327378227202*t+1) -10*(1934765206983839058236946310427822300047948801*t^2+ 22610808899118991129157653040129843043806131198*t+1)/(t-1)/(t^2-\ 266074023310154679231357456960045092327378227202*t+1) 20*(551369855667675151263762766588308130756113121*t^2-\ 12824156908719090244961062441867140802683153122*t+1)/(t-1)/(t^2-\ 266074023310154679231357456960045092327378227202*t+1) Then for all i>=0 we have 3 3 3 40 a(i) + 61 b(i) + 61 c(i) = -1080 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 560, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 9 (6378340833753612334484632371359592412041108935677 t / ----- i = 0 / + 42284925366567369046218843018615144964902460369926 t - 3) / ((t - 1) / 2 (t - 64598221479972845810852671325010694375542320332802 t + 1)) infinity ----- \ i 2 ) b(i) t = - 2 (23211078503419603237908662279164075788672937904641 t / ----- i = 0 / + 127913899402184362070737477600426749806518857807358 t + 1) / ((t - 1) / 2 (t - 64598221479972845810852671325010694375542320332802 t + 1)) infinity ----- \ i 2 ) c(i) t = 22 (736771071990717255829933620061893691114525923841 t / ----- i = 0 / - 14475405427045623192979582700024696017950143715842 t + 1) / ((t - 1) / 2 (t - 64598221479972845810852671325010694375542320332802 t + 1)) In Maple notation, these generating functions are 9*(6378340833753612334484632371359592412041108935677*t^2+ 42284925366567369046218843018615144964902460369926*t-3)/(t-1)/(t^2-\ 64598221479972845810852671325010694375542320332802*t+1) -2*(23211078503419603237908662279164075788672937904641*t^2+ 127913899402184362070737477600426749806518857807358*t+1)/(t-1)/(t^2-\ 64598221479972845810852671325010694375542320332802*t+1) 22*(736771071990717255829933620061893691114525923841*t^2-\ 14475405427045623192979582700024696017950143715842*t+1)/(t-1)/(t^2-\ 64598221479972845810852671325010694375542320332802*t+1) Then for all i>=0 we have 3 3 3 40 a(i) + 79 b(i) + 79 c(i) = -53240 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 561, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 2 (27001497463482672930449136200792965524914466442584841 t / ----- i = 0 / + 294129043530749570671187638603862554040449108293152290 t - 11) / ( / 2 (t - 1) (t - 238051367766370203280430548524468710002660904324652098 t + 1) ) infinity ----- \ i 2 ) b(i) t = - 8 (5692068330847564664873661414909184497047768232412079 t / ----- i = 0 / + 36727327984437516437103799053416153214619631561447520 t + 1) / ( / 2 (t - 1) (t - 238051367766370203280430548524468710002660904324652098 t + 1) ) infinity ----- \ i 2 ) c(i) t = 2 (12767718707285564981550521140824528534519048321283561 t / ----- i = 0 / - 182445303968425889389460363014125879381188647496721970 t + 9) / ( / 2 (t - 1) (t - 238051367766370203280430548524468710002660904324652098 t + 1) ) In Maple notation, these generating functions are 2*(27001497463482672930449136200792965524914466442584841*t^2+ 294129043530749570671187638603862554040449108293152290*t-11)/(t-1)/(t^2-\ 238051367766370203280430548524468710002660904324652098*t+1) -8*(5692068330847564664873661414909184497047768232412079*t^2+ 36727327984437516437103799053416153214619631561447520*t+1)/(t-1)/(t^2-\ 238051367766370203280430548524468710002660904324652098*t+1) 2*(12767718707285564981550521140824528534519048321283561*t^2-\ 182445303968425889389460363014125879381188647496721970*t+9)/(t-1)/(t^2-\ 238051367766370203280430548524468710002660904324652098*t+1) Then for all i>=0 we have 3 3 3 40 a(i) + 81 b(i) + 81 c(i) = -5000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 562, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 4 (1860431118116222812783187 t + 25813915879824240841389380 t - 7) ------------------------------------------------------------------- 2 (t - 1) (t - 42067955436549711461522498 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 12 (503815716513040577864349 t + 3549683843771181794917250 t + 1) - ------------------------------------------------------------------ 2 (t - 1) (t - 42067955436549711461522498 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 2 (1895360288098714489741739 t - 26216357649804048726431350 t + 11) -------------------------------------------------------------------- 2 (t - 1) (t - 42067955436549711461522498 t + 1) In Maple notation, these generating functions are 4*(1860431118116222812783187*t^2+25813915879824240841389380*t-7)/(t-1)/(t^2-\ 42067955436549711461522498*t+1) -12*(503815716513040577864349*t^2+3549683843771181794917250*t+1)/(t-1)/(t^2-\ 42067955436549711461522498*t+1) 2*(1895360288098714489741739*t^2-26216357649804048726431350*t+11)/(t-1)/(t^2-\ 42067955436549711461522498*t+1) Then for all i>=0 we have 3 3 3 40 a(i) + 99 b(i) + 99 c(i) = -5000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 563, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = (55464889927143005976087163667993271412525135609047738221\ / ----- i = 0 2 6082968661804782394758147 t + 13699152436484830490298471209457196814884\ / 2 72002907735720945470571325571910855752266 t - 13) / ((t - 1) (t - 472\ / 625849338269236484481626581138398703328963178323700735242260471587910676\ 144002 t + 1)) infinity ----- \ i ) b(i) t = - 9 (7439419712125963887393019562296665635443367628746376\ / ----- i = 0 2 3392281704390708737442123041 t + 16170420936296980184269356286156511665\ / 2 254499338326755798884829319768722536601758 t + 1) / ((t - 1) (t - 472\ / 625849338269236484481626581138398703328963178323700735242260471587910676\ 144002 t + 1)) infinity ----- \ i ) c(i) t = 15 (34071777334252353614627229056066989734083989465992974\ / ----- i = 0 2 564586489898009913276802241 t - 884105481687863250495469602015408905458\ / 2 96894841467286079286410124296389264037122 t + 1) / ((t - 1) (t - 4726\ / 258493382692364844816265811383987033289631783237007352422604715879106761\ 44002 t + 1)) In Maple notation, these generating functions are (554648899271430059760871636679932714125251356090477382216082968661804782394758\ 147*t^2+13699152436484830490298471209457196814884720029077357209454705713255719\ 10855752266*t-13)/(t-1)/(t^2-47262584933826923648448162658113839870332896317832\ 3700735242260471587910676144002*t+1) -9*(743941971212596388739301956229666563544336762874637633922817043907087374421\ 23041*t^2+161704209362969801842693562861565116652544993383267557988848293197687\ 22536601758*t+1)/(t-1)/(t^2-472625849338269236484481626581138398703328963178323\ 700735242260471587910676144002*t+1) 15*(340717773342523536146272290560669897340839894659929745645864898980099132768\ 02241*t^2-884105481687863250495469602015408905458968948414672860792864101242963\ 89264037122*t+1)/(t-1)/(t^2-472625849338269236484481626581138398703328963178323\ 700735242260471587910676144002*t+1) Then for all i>=0 we have 3 3 3 42 a(i) + 43 b(i) + 43 c(i) = -21504 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 564, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 16 (11079875534802356285029787818572035753726096296074395\ / ----- i = 0 2 924866925522761786760999 t + 741675490075667272914517788346140966878256\ / 2 29069986010902736762346939408864002 t - 1) / ((t - 1) (t - 5306370420\ / 90747307424198411023261815872787776769541393482266793850947456000002 t + 1) ) infinity ----- \ i ) b(i) t = - 3 (5874145976633093731407093060341369657821604696245693\ / ----- i = 0 2 2637298573652587551717003 t + 13255111181136629479758131328074283668029\ / 2 6643023479899584272520403124658282994 t + 3) / ((t - 1) (t - 53063704\ / 2090747307424198411023261815872787776769541393482266793850947456000002 t + 1)) infinity ----- \ i ) c(i) t = 15 (83715679807549931664241555474036427049838276641639515\ / ----- i = 0 2 78928842190247251521001 t - 4663008229629443958875460432423494935668636\ / 2 5661351318023243061001389693521002 t + 1) / ((t - 1) (t - 53063704209\ / 0747307424198411023261815872787776769541393482266793850947456000002 t + 1)) In Maple notation, these generating functions are 16*( 11079875534802356285029787818572035753726096296074395924866925522761786760999*t ^2+ 74167549007566727291451778834614096687825629069986010902736762346939408864002*t -1)/(t-1)/(t^2-\ 530637042090747307424198411023261815872787776769541393482266793850947456000002* t+1) -3*( 58741459766330937314070930603413696578216046962456932637298573652587551717003*t ^2+ 132551111811366294797581313280742836680296643023479899584272520403124658282994* t+3)/(t-1)/(t^2-\ 530637042090747307424198411023261815872787776769541393482266793850947456000002* t+1) 15*( 8371567980754993166424155547403642704983827664163951578928842190247251521001*t^ 2-46630082296294439588754604324234949356686365661351318023243061001389693521002 *t+1)/(t-1)/(t^2-\ 530637042090747307424198411023261815872787776769541393482266793850947456000002* t+1) Then for all i>=0 we have 3 3 3 42 a(i) + 67 b(i) + 67 c(i) = -5250 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 565, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 5 ( / ----- i = 0 2 7004020214882507491033840868715514981094895814240998860798945215785599 t + 8641741965953224381732442237536028351062601045074026872500168775894402 t / 2 - 1) / ((t - 1) (t - / 28111491398086965397409337938874724198429323625273338919179708879360002 t + 1)) infinity ----- \ i ) b(i) t = - ( / ----- i = 0 2 34785586774116106365886747980127726598716020016894319640519497404267201 t + 19910980199537265221832778326280107814517505588841136175079031184532798 t / 2 + 1) / ((t - 1) (t - / 28111491398086965397409337938874724198429323625273338919179708879360002 t + 1)) infinity ----- \ i ) c(i) t = 6 ( / ----- i = 0 2 2879256039484972939717024301389823190996463413548637081420355727467201 t - 11995350535093868204336945352457795593202051014504546384020110492267202 t / 2 + 1) / ((t - 1) (t - / 28111491398086965397409337938874724198429323625273338919179708879360002 t + 1)) In Maple notation, these generating functions are 5*(7004020214882507491033840868715514981094895814240998860798945215785599*t^2+ 8641741965953224381732442237536028351062601045074026872500168775894402*t-1)/(t-\ 1)/(t^2-28111491398086965397409337938874724198429323625273338919179708879360002 *t+1) -(34785586774116106365886747980127726598716020016894319640519497404267201*t^2+ 19910980199537265221832778326280107814517505588841136175079031184532798*t+1)/(t -1)/(t^2-\ 28111491398086965397409337938874724198429323625273338919179708879360002*t+1) 6*(2879256039484972939717024301389823190996463413548637081420355727467201*t^2-\ 11995350535093868204336945352457795593202051014504546384020110492267202*t+1)/(t -1)/(t^2-\ 28111491398086965397409337938874724198429323625273338919179708879360002*t+1) Then for all i>=0 we have 3 3 3 43 a(i) + 50 b(i) + 50 c(i) = -5375 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 566, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 27 ( / ----- i = 0 2 25465071971470381854262099292253454270916419189550922559 t / + 72260482658364903570573526489088344336518732807289397442 t - 1) / ( / (t - 1) 2 (t - 350282379290592214366236912583209472921606692635631129602 t + 1)) infinity ----- \ i ) b(i) t = - 2 ( / ----- i = 0 2 462174228815548804234021201349566401862116259338897057133 t / - 133306492800363974152183051981050957852747530445182241146 t + 13) / ( / (t - 1) 2 (t - 350282379290592214366236912583209472921606692635631129602 t + 1)) infinity ----- \ i ) c(i) t = 3 ( / ----- i = 0 2 269918544586493630041287651961330753168369544108271654251 t / - 489163701929950183429179751540341049174615363370748198262 t + 11) / ( / (t - 1) 2 (t - 350282379290592214366236912583209472921606692635631129602 t + 1)) In Maple notation, these generating functions are 27*(25465071971470381854262099292253454270916419189550922559*t^2+ 72260482658364903570573526489088344336518732807289397442*t-1)/(t-1)/(t^2-\ 350282379290592214366236912583209472921606692635631129602*t+1) -2*(462174228815548804234021201349566401862116259338897057133*t^2-\ 133306492800363974152183051981050957852747530445182241146*t+13)/(t-1)/(t^2-\ 350282379290592214366236912583209472921606692635631129602*t+1) 3*(269918544586493630041287651961330753168369544108271654251*t^2-\ 489163701929950183429179751540341049174615363370748198262*t+11)/(t-1)/(t^2-\ 350282379290592214366236912583209472921606692635631129602*t+1) Then for all i>=0 we have 3 3 3 43 a(i) + 54 b(i) + 54 c(i) = -145125 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 567, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (11400357385543619181764583177846567645287404201 t / ----- i = 0 / + 33336446882415798015314933662921370849946739054 t - 23) / ((t - 1) / 2 (t - 6635228802571534474181257275151244345640993794 t + 1)) infinity ----- \ i 2 ) b(i) t = - (11740930376595403055600975776388314753710913355 t / ----- i = 0 / + 10091532740302824504638334459900704411050263722 t + 11) / ((t - 1) / 2 (t - 6635228802571534474181257275151244345640993794 t + 1)) infinity ----- \ i 2 ) c(i) t = (7940811248080863328346114717106125538615111959 t / ----- i = 0 / - 29773274364979090888585424953395144703376289070 t + 23) / ((t - 1) / 2 (t - 6635228802571534474181257275151244345640993794 t + 1)) In Maple notation, these generating functions are (11400357385543619181764583177846567645287404201*t^2+ 33336446882415798015314933662921370849946739054*t-23)/(t-1)/(t^2-\ 6635228802571534474181257275151244345640993794*t+1) -(11740930376595403055600975776388314753710913355*t^2+ 10091532740302824504638334459900704411050263722*t+11)/(t-1)/(t^2-\ 6635228802571534474181257275151244345640993794*t+1) (7940811248080863328346114717106125538615111959*t^2-\ 29773274364979090888585424953395144703376289070*t+23)/(t-1)/(t^2-\ 6635228802571534474181257275151244345640993794*t+1) Then for all i>=0 we have 3 3 3 43 a(i) + 57 b(i) + 57 c(i) = -94471 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 568, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = (94141652227347042269284801566079821950030262543251291270\ / ----- i = 0 2 289297850995175256617 t + 104631633998887370605841422434960969938909333\ / 2 322317036759350705911634363870702 t - 23) / ((t - 1) (t - 17907390368\ / 004600680781450895062873005251209336268890477515796581565856223234 t + 1)) infinity ----- \ i ) b(i) t = - (108116233736525650738374164361040411792335862944735098\ / ----- i = 0 2 014073557033752657864403 t - 488426463042920879531423499917980119918892\ / 2 42818386706160574804178044820260582 t + 19) / ((t - 1) (t - 179073903\ / 68004600680781450895062873005251209336268890477515796581565856223234 t + 1) ) infinity ----- \ i ) c(i) t = 4 (223219758227640605711293010119561118505824526090212099\ / ----- i = 0 2 40003924365888405703271 t - 3714037268082245126743725460426671180069410\ / 2 7640608307903378612579815365104238 t + 7) / ((t - 1) (t - 17907390368\ / 004600680781450895062873005251209336268890477515796581565856223234 t + 1)) In Maple notation, these generating functions are (94141652227347042269284801566079821950030262543251291270289297850995175256617* t^2+ 104631633998887370605841422434960969938909333322317036759350705911634363870702* t-23)/(t-1)/(t^2-\ 17907390368004600680781450895062873005251209336268890477515796581565856223234*t +1) -( 108116233736525650738374164361040411792335862944735098014073557033752657864403* t^2-\ 48842646304292087953142349991798011991889242818386706160574804178044820260582*t +19)/(t-1)/(t^2-\ 17907390368004600680781450895062873005251209336268890477515796581565856223234*t +1) 4*( 22321975822764060571129301011956111850582452609021209940003924365888405703271*t ^2-\ 37140372680822451267437254604266711800694107640608307903378612579815365104238*t +7)/(t-1)/(t^2-\ 17907390368004600680781450895062873005251209336268890477515796581565856223234*t +1) Then for all i>=0 we have 3 3 3 43 a(i) + 65 b(i) + 65 c(i) = -457864 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 569, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 26 (5166450992639 t + 38868555586562 t - 1) ) a(i) t = -------------------------------------------- / 2 ----- (t - 1) (t - 263766767846402 t + 1) i = 0 infinity ----- 2 \ i 9 (13603137136161 t + 60858660892638 t + 1) ) b(i) t = - -------------------------------------------- / 2 ----- (t - 1) (t - 263766767846402 t + 1) i = 0 infinity ----- 2 \ i 67116817716023 t - 737272999975246 t + 23 ) c(i) t = ------------------------------------------ / 2 ----- (t - 1) (t - 263766767846402 t + 1) i = 0 In Maple notation, these generating functions are 26*(5166450992639*t^2+38868555586562*t-1)/(t-1)/(t^2-263766767846402*t+1) -9*(13603137136161*t^2+60858660892638*t+1)/(t-1)/(t^2-263766767846402*t+1) (67116817716023*t^2-737272999975246*t+23)/(t-1)/(t^2-263766767846402*t+1) Then for all i>=0 we have 3 3 3 43 a(i) + 68 b(i) + 68 c(i) = -22016 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 570, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 24 (28887792172419719875542811001637185655033932773860542\ / ----- i = 0 2 8740876703794049084158832981019 t + 52432048389577593769578985429698207\ / 2 8866296588834474873154276097010846123693814707782 t - 1) / ((t - 1) (t / - 210114500289263979465420600725490099896597710299023275932203967370840\ 1083273565318402 t + 1)) infinity ----- \ i ) b(i) t = - (652109803546897333512711227378085481793985964215226418\ / ----- i = 0 2 5155618060043043469776766146291 t + 16699550769520083189593076225203898\ / 2 15115404622358895373884436417966771456992908176898 t + 11) / ((t - 1) (t / - 210114500289263979465420600725490099896597710299023275932203967370840\ 1083273565318402 t + 1)) infinity ----- \ i ) c(i) t = (45402208579316211150898909479543049444518185376589698166\ / ----- i = 0 2 46749234026706892687625705023 t - 1273127397035260276917631084425554957\ / 2 7507082802170129375686803712036521819457300028246 t + 23) / ((t - 1) (t / - 210114500289263979465420600725490099896597710299023275932203967370840\ 1083273565318402 t + 1)) In Maple notation, these generating functions are 24*(288877921724197198755428110016371856550339327738605428740876703794049084158\ 832981019*t^2+52432048389577593769578985429698207886629658883447487315427609701\ 0846123693814707782*t-1)/(t-1)/(t^2-2101145002892639794654206007254900998965977\ 102990232759322039673708401083273565318402*t+1) -(65210980354689733351271122737808548179398596421522641851556180600430434697767\ 66146291*t^2+166995507695200831895930762252038981511540462235889537388443641796\ 6771456992908176898*t+11)/(t-1)/(t^2-210114500289263979465420600725490099896597\ 7102990232759322039673708401083273565318402*t+1) (454022085793162111508989094795430494445181853765896981664674923402670689268762\ 5705023*t^2-1273127397035260276917631084425554957750708280217012937568680371203\ 6521819457300028246*t+23)/(t-1)/(t^2-210114500289263979465420600725490099896597\ 7102990232759322039673708401083273565318402*t+1) Then for all i>=0 we have 3 3 3 43 a(i) + 78 b(i) + 78 c(i) = -250776 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 571, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 4 (424193767 t + 12618113836 t - 3) ) a(i) t = ------------------------------------ / 2 ----- (t - 1) (t - 104263118402 t + 1) i = 0 infinity ----- 2 \ i 8 (311621147 t + 440457451 t + 2) ) b(i) t = - ---------------------------------- / 2 ----- (t - 1) (t - 104263118402 t + 1) i = 0 infinity ----- 2 \ i 2362448017 t - 8379076834 t + 17 ) c(i) t = --------------------------------- / 2 ----- (t - 1) (t - 104263118402 t + 1) i = 0 In Maple notation, these generating functions are 4*(424193767*t^2+12618113836*t-3)/(t-1)/(t^2-104263118402*t+1) -8*(311621147*t^2+440457451*t+2)/(t-1)/(t^2-104263118402*t+1) (2362448017*t^2-8379076834*t+17)/(t-1)/(t^2-104263118402*t+1) Then for all i>=0 we have 3 3 3 43 a(i) + 91 b(i) + 91 c(i) = -43 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 572, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 8 (502601774 t + 667460939 t - 1) ) a(i) t = ---------------------------------- / 2 ----- (t - 1) (t - 2639287874 t + 1) i = 0 infinity ----- 2 \ i 3886651397 t - 1103099722 t + 5 ) b(i) t = - -------------------------------- / 2 ----- (t - 1) (t - 2639287874 t + 1) i = 0 infinity ----- 2 \ i 8 (385311070 t - 733255031 t + 1) ) c(i) t = ---------------------------------- / 2 ----- (t - 1) (t - 2639287874 t + 1) i = 0 In Maple notation, these generating functions are 8*(502601774*t^2+667460939*t-1)/(t-1)/(t^2-2639287874*t+1) -(3886651397*t^2-1103099722*t+5)/(t-1)/(t^2-2639287874*t+1) 8*(385311070*t^2-733255031*t+1)/(t-1)/(t^2-2639287874*t+1) Then for all i>=0 we have 3 3 3 43 a(i) + 95 b(i) + 95 c(i) = -14749 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 573, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 28 / ----- i = 0 2 (903433171804046059682735736359 t + 3205281691099465068181768146842 t - 1) / 2 / ((t - 1) (t - 15796612482619324336255762502402 t + 1)) / infinity ----- \ i 2 ) b(i) t = - (21591825811424433419471926659011 t / ----- i = 0 / + 26436258605428259764497613878578 t + 11) / ((t - 1) / 2 (t - 15796612482619324336255762502402 t + 1)) infinity ----- \ i ) c(i) t = 23 / ----- i = 0 2 (624537410304002823565653946441 t - 2712714993645424266346938317642 t + 1) / 2 / ((t - 1) (t - 15796612482619324336255762502402 t + 1)) / In Maple notation, these generating functions are 28*(903433171804046059682735736359*t^2+3205281691099465068181768146842*t-1)/(t-\ 1)/(t^2-15796612482619324336255762502402*t+1) -(21591825811424433419471926659011*t^2+26436258605428259764497613878578*t+11)/( t-1)/(t^2-15796612482619324336255762502402*t+1) 23*(624537410304002823565653946441*t^2-2712714993645424266346938317642*t+1)/(t-\ 1)/(t^2-15796612482619324336255762502402*t+1) Then for all i>=0 we have 3 3 3 43 a(i) + 98 b(i) + 98 c(i) = -117992 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 574, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 26 (123546168359 t + 194385700442 t - 1) ) a(i) t = ----------------------------------------- / 2 ----- (t - 1) (t - 767547705602 t + 1) i = 0 infinity ----- 2 \ i 16 (231945244246 t + 11253529753 t + 1) ) b(i) t = - ---------------------------------------- / 2 ----- (t - 1) (t - 767547705602 t + 1) i = 0 infinity ----- 2 \ i 2685953574751 t - 6577133958782 t + 31 ) c(i) t = --------------------------------------- / 2 ----- (t - 1) (t - 767547705602 t + 1) i = 0 In Maple notation, these generating functions are 26*(123546168359*t^2+194385700442*t-1)/(t-1)/(t^2-767547705602*t+1) -16*(231945244246*t^2+11253529753*t+1)/(t-1)/(t^2-767547705602*t+1) (2685953574751*t^2-6577133958782*t+31)/(t-1)/(t^2-767547705602*t+1) Then for all i>=0 we have 3 3 3 45 a(i) + 47 b(i) + 47 c(i) = -416745 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 575, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 16 (96246377547767 t + 222053102523146 t - 1) ) a(i) t = ---------------------------------------------- / 2 ----- (t - 1) (t - 723319186424834 t + 1) i = 0 infinity ----- 2 \ i 1402829072119297 t + 2286266084550142 t + 1 ) b(i) t = - -------------------------------------------- / 2 ----- (t - 1) (t - 723319186424834 t + 1) i = 0 infinity ----- 2 \ i 16 (36116257606867 t - 266684704898708 t + 1) ) c(i) t = ---------------------------------------------- / 2 ----- (t - 1) (t - 723319186424834 t + 1) i = 0 In Maple notation, these generating functions are 16*(96246377547767*t^2+222053102523146*t-1)/(t-1)/(t^2-723319186424834*t+1) -(1402829072119297*t^2+2286266084550142*t+1)/(t-1)/(t^2-723319186424834*t+1) 16*(36116257606867*t^2-266684704898708*t+1)/(t-1)/(t^2-723319186424834*t+1) Then for all i>=0 we have 3 3 3 45 a(i) + 64 b(i) + 64 c(i) = -77760 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 576, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 20 (2713466715162565163880275236268496924268655 t / ----- i = 0 / + 191873897067731488383280902976397348065409426 t - 1) / ((t - 1) / 2 (t - 2510606680984342835987032236245436296554521602 t + 1)) infinity ----- \ i 2 ) b(i) t = - (43444758595682402601054098336907464295050881 t / ----- i = 0 / + 2995064549686101714302566823280429862830837118 t + 1) / ((t - 1) / 2 (t - 2510606680984342835987032236245436296554521602 t + 1)) infinity ----- \ i 2 ) c(i) t = 16 (402683734534782125167919296964247548893531 t / ----- i = 0 / - 190309515502146289431644226898047830494261532 t + 1) / ((t - 1) / 2 (t - 2510606680984342835987032236245436296554521602 t + 1)) In Maple notation, these generating functions are 20*(2713466715162565163880275236268496924268655*t^2+ 191873897067731488383280902976397348065409426*t-1)/(t-1)/(t^2-\ 2510606680984342835987032236245436296554521602*t+1) -(43444758595682402601054098336907464295050881*t^2+ 2995064549686101714302566823280429862830837118*t+1)/(t-1)/(t^2-\ 2510606680984342835987032236245436296554521602*t+1) 16*(402683734534782125167919296964247548893531*t^2-\ 190309515502146289431644226898047830494261532*t+1)/(t-1)/(t^2-\ 2510606680984342835987032236245436296554521602*t+1) Then for all i>=0 we have 3 3 3 45 a(i) + 88 b(i) + 88 c(i) = -360 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 577, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 17 (18515770602491433229243806702441997681827302654554319 t / ----- i = 0 / + 23304979945256420693649311351620076785462116065970482 t - 1) / ( / 2 (t - 1) (t - 83918827027509950908935394715909706457571472843705602 t + 1)) infinity ----- \ i ) b(i) t = - 6 ( / ----- i = 0 2 48811250678814656473190592373456209887619255253014001 t / + 13420688465181486897480599213622898271928129102992398 t + 1) / ( / 2 (t - 1) (t - 83918827027509950908935394715909706457571472843705602 t + 1)) infinity ----- \ i 2 ) c(i) t = 18 (9911465372890655897181819398394212172821284172672881 t / ----- i = 0 / - 30655445087556037020738883260753914892670412291341682 t + 1) / ( / 2 (t - 1) (t - 83918827027509950908935394715909706457571472843705602 t + 1)) In Maple notation, these generating functions are 17*(18515770602491433229243806702441997681827302654554319*t^2+ 23304979945256420693649311351620076785462116065970482*t-1)/(t-1)/(t^2-\ 83918827027509950908935394715909706457571472843705602*t+1) -6*(48811250678814656473190592373456209887619255253014001*t^2+ 13420688465181486897480599213622898271928129102992398*t+1)/(t-1)/(t^2-\ 83918827027509950908935394715909706457571472843705602*t+1) 18*(9911465372890655897181819398394212172821284172672881*t^2-\ 30655445087556037020738883260753914892670412291341682*t+1)/(t-1)/(t^2-\ 83918827027509950908935394715909706457571472843705602*t+1) Then for all i>=0 we have 3 3 3 48 a(i) + 77 b(i) + 77 c(i) = -196608 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 578, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 27 (22014677346742079 t + 35620529190966722 t - 1) ) a(i) t = --------------------------------------------------- / 2 ----- (t - 1) (t - 147639149571513602 t + 1) i = 0 infinity ----- 2 \ i 849763517424822029 t - 461715790964828458 t + 29 ) b(i) t = - ------------------------------------------------- / 2 ----- (t - 1) (t - 147639149571513602 t + 1) i = 0 infinity ----- 2 \ i 750697469364482677 t - 1138745195824476314 t + 37 ) c(i) t = -------------------------------------------------- / 2 ----- (t - 1) (t - 147639149571513602 t + 1) i = 0 In Maple notation, these generating functions are 27*(22014677346742079*t^2+35620529190966722*t-1)/(t-1)/(t^2-147639149571513602* t+1) -(849763517424822029*t^2-461715790964828458*t+29)/(t-1)/(t^2-147639149571513602 *t+1) (750697469364482677*t^2-1138745195824476314*t+37)/(t-1)/(t^2-147639149571513602 *t+1) Then for all i>=0 we have 3 3 3 49 a(i) + 54 b(i) + 54 c(i) = -453789 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 579, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 4 (17079462032587249913 t + 32748834278854813454 t - 7) ) a(i) t = -------------------------------------------------------- / 2 ----- (t - 1) (t - 19629328849962024962 t + 1) i = 0 infinity ----- 2 \ i 77389243570792350739 t - 3401773290166256678 t + 19 ) b(i) t = - ---------------------------------------------------- / 2 ----- (t - 1) (t - 19629328849962024962 t + 1) i = 0 infinity ----- 2 \ i 60309781538205100831 t - 134297251818831194942 t + 31 ) c(i) t = ------------------------------------------------------ / 2 ----- (t - 1) (t - 19629328849962024962 t + 1) i = 0 In Maple notation, these generating functions are 4*(17079462032587249913*t^2+32748834278854813454*t-7)/(t-1)/(t^2-\ 19629328849962024962*t+1) -(77389243570792350739*t^2-3401773290166256678*t+19)/(t-1)/(t^2-\ 19629328849962024962*t+1) (60309781538205100831*t^2-134297251818831194942*t+31)/(t-1)/(t^2-\ 19629328849962024962*t+1) Then for all i>=0 we have 3 3 3 49 a(i) + 64 b(i) + 64 c(i) = -392000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 580, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 22 (1179315126157246698935681183 t + 3883795503537793764192367202 t - 1) ------------------------------------------------------------------------- 2 (t - 1) (t - 17278073898035220590344561154 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 7 (3559417014814152115356378097 t + 5814857121353893098553968910 t + 1) - ------------------------------------------------------------------------ 2 (t - 1) (t - 17278073898035220590344561154 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 21 (677748166203552129107322385 t - 3802506211592900533744104722 t + 1) ------------------------------------------------------------------------ 2 (t - 1) (t - 17278073898035220590344561154 t + 1) In Maple notation, these generating functions are 22*(1179315126157246698935681183*t^2+3883795503537793764192367202*t-1)/(t-1)/(t ^2-17278073898035220590344561154*t+1) -7*(3559417014814152115356378097*t^2+5814857121353893098553968910*t+1)/(t-1)/(t ^2-17278073898035220590344561154*t+1) 21*(677748166203552129107322385*t^2-3802506211592900533744104722*t+1)/(t-1)/(t^ 2-17278073898035220590344561154*t+1) Then for all i>=0 we have 3 3 3 49 a(i) + 68 b(i) + 68 c(i) = -84672 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 581, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (12520861 t + 15232750 t - 11) ) a(i) t = --------------------------------- / 2 ----- (t - 1) (t - 5522498 t + 1) i = 0 infinity ----- 2 \ i 7 (4468187 t - 2492510 t + 3) ) b(i) t = - ------------------------------ / 2 ----- (t - 1) (t - 5522498 t + 1) i = 0 infinity ----- 2 \ i 28 (967989 t - 1461910 t + 1) ) c(i) t = ------------------------------ / 2 ----- (t - 1) (t - 5522498 t + 1) i = 0 In Maple notation, these generating functions are 2*(12520861*t^2+15232750*t-11)/(t-1)/(t^2-5522498*t+1) -7*(4468187*t^2-2492510*t+3)/(t-1)/(t^2-5522498*t+1) 28*(967989*t^2-1461910*t+1)/(t-1)/(t^2-5522498*t+1) Then for all i>=0 we have 3 3 3 49 a(i) + 72 b(i) + 72 c(i) = -392000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 582, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 9 (835931446382467689289951402271759935552442273418367877\ / ----- i = 0 2 149332706945692262208317 t + 600611114776652164524154791550685054812816\ / 2 27399997715782530997965022280058681286 t - 3) / ((t - 1) (t - 1076461\ / 717169697342928331722385045031971295624794165970324519417984069015449222\ 402 t + 1)) infinity ----- \ i ) b(i) t = - 21 (375939746646331515181498008367013538452287349842699\ / ----- i = 0 2 598400228480401157250350001 t + 929391205981870717650707697616338777537\ / 2 3916530246054706728595293597537787371598 t + 1) / ((t - 1) (t - 10764\ / 617171696973429283317223850450319712956247941659703245194179840690154492\ 22402 t + 1)) infinity ----- \ i ) c(i) t = 28 (21478174732901462563960955430699373044660854398233442\ / ----- i = 0 2 2957814267778446238120761 t - 74671706021777936444060407927047947158162\ / 2 61454048900151804432098277467516411962 t + 1) / ((t - 1) (t - 1076461\ / 717169697342928331722385045031971295624794165970324519417984069015449222\ 402 t + 1)) In Maple notation, these generating functions are 9*( 835931446382467689289951402271759935552442273418367877149332706945692262208317* t^2+600611114776652164524154791550685054812816273999977157825309979650222800586\ 81286*t-3)/(t-1)/(t^2-107646171716969734292833172238504503197129562479416597032\ 4519417984069015449222402*t+1) -21*( 375939746646331515181498008367013538452287349842699598400228480401157250350001* t^2+929391205981870717650707697616338777537391653024605470672859529359753778737\ 1598*t+1)/(t-1)/(t^2-1076461717169697342928331722385045031971295624794165970324\ 519417984069015449222402*t+1) 28*( 214781747329014625639609554306993730446608543982334422957814267778446238120761* t^2-746717060217779364440604079270479471581626145404890015180443209827746751641\ 1962*t+1)/(t-1)/(t^2-1076461717169697342928331722385045031971295624794165970324\ 519417984069015449222402*t+1) Then for all i>=0 we have 3 3 3 49 a(i) + 76 b(i) + 76 c(i) = -49 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 583, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 16 (60467236367 t + 325916764658 t - 1) ) a(i) t = ---------------------------------------- / 2 ----- (t - 1) (t - 1973817065474 t + 1) i = 0 infinity ----- 2 \ i 7 (126782218753 t + 282877926910 t + 1) ) b(i) t = - ---------------------------------------- / 2 ----- (t - 1) (t - 1973817065474 t + 1) i = 0 infinity ----- 2 \ i 14 (41403023425 t - 246233096258 t + 1) ) c(i) t = ---------------------------------------- / 2 ----- (t - 1) (t - 1973817065474 t + 1) i = 0 In Maple notation, these generating functions are 16*(60467236367*t^2+325916764658*t-1)/(t-1)/(t^2-1973817065474*t+1) -7*(126782218753*t^2+282877926910*t+1)/(t-1)/(t^2-1973817065474*t+1) 14*(41403023425*t^2-246233096258*t+1)/(t-1)/(t^2-1973817065474*t+1) Then for all i>=0 we have 3 3 3 49 a(i) + 88 b(i) + 88 c(i) = -10584 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 584, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 3128531807564249032883347 t + 93633181720804390436366218 t - 29 ---------------------------------------------------------------- 2 (t - 1) (t - 36650212105114483201980674 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 4 (623145266389954305972545 t + 16891584570836200517005758 t + 1) - ------------------------------------------------------------------ 2 (t - 1) (t - 36650212105114483201980674 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 691305176356158689805831 t - 70750224525260777981719070 t + 23 --------------------------------------------------------------- 2 (t - 1) (t - 36650212105114483201980674 t + 1) In Maple notation, these generating functions are (3128531807564249032883347*t^2+93633181720804390436366218*t-29)/(t-1)/(t^2-\ 36650212105114483201980674*t+1) -4*(623145266389954305972545*t^2+16891584570836200517005758*t+1)/(t-1)/(t^2-\ 36650212105114483201980674*t+1) (691305176356158689805831*t^2-70750224525260777981719070*t+23)/(t-1)/(t^2-\ 36650212105114483201980674*t+1) Then for all i>=0 we have 3 3 3 49 a(i) + 99 b(i) + 99 c(i) = -3136 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 585, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 387658485742867138771 t + 485938188135520520458 t - 29 ) a(i) t = ------------------------------------------------------- / 2 ----- (t - 1) (t - 66735382635101980802 t + 1) i = 0 infinity ----- 2 \ i 25 (18308883786300900937 t - 8822641523060758538 t + 1) ) b(i) t = - -------------------------------------------------------- / 2 ----- (t - 1) (t - 66735382635101980802 t + 1) i = 0 infinity ----- 2 \ i 5 (77447746722672972367 t - 124878958038873684374 t + 7) ) c(i) t = --------------------------------------------------------- / 2 ----- (t - 1) (t - 66735382635101980802 t + 1) i = 0 In Maple notation, these generating functions are (387658485742867138771*t^2+485938188135520520458*t-29)/(t-1)/(t^2-\ 66735382635101980802*t+1) -25*(18308883786300900937*t^2-8822641523060758538*t+1)/(t-1)/(t^2-\ 66735382635101980802*t+1) 5*(77447746722672972367*t^2-124878958038873684374*t+7)/(t-1)/(t^2-\ 66735382635101980802*t+1) Then for all i>=0 we have 3 3 3 50 a(i) + 77 b(i) + 77 c(i) = -878800 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 586, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 28 (158568278891791103124993156369415999 t / ----- i = 0 / + 1419030750371296488770430398916604002 t - 1) / ((t - 1) / 2 (t - 12227338279564266419678678490849920002 t + 1)) infinity ----- \ i 2 ) b(i) t = - 5 (834027028581502405854602188355226203 t / ----- i = 0 / + 2873519850741820951597472354043573794 t + 3) / ((t - 1) / 2 (t - 12227338279564266419678678490849920002 t + 1)) infinity ----- \ i 2 ) c(i) t = 25 (116063556470927328170922627632832121 t / ----- i = 0 / - 857572932335591999661337536112592122 t + 1) / ((t - 1) / 2 (t - 12227338279564266419678678490849920002 t + 1)) In Maple notation, these generating functions are 28*(158568278891791103124993156369415999*t^2+ 1419030750371296488770430398916604002*t-1)/(t-1)/(t^2-\ 12227338279564266419678678490849920002*t+1) -5*(834027028581502405854602188355226203*t^2+ 2873519850741820951597472354043573794*t+3)/(t-1)/(t^2-\ 12227338279564266419678678490849920002*t+1) 25*(116063556470927328170922627632832121*t^2-\ 857572932335591999661337536112592122*t+1)/(t-1)/(t^2-\ 12227338279564266419678678490849920002*t+1) Then for all i>=0 we have 3 3 3 50 a(i) + 91 b(i) + 91 c(i) = -17150 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 587, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 128642502971265742339 t + 742963079133429834010 t - 29 ) a(i) t = ------------------------------------------------------- / 2 ----- (t - 1) (t - 108819844766059504898 t + 1) i = 0 infinity ----- 2 \ i 2 (61220503655255586097 t + 292606000306947971278 t + 1) ) b(i) t = - --------------------------------------------------------- / 2 ----- (t - 1) (t - 108819844766059504898 t + 1) i = 0 infinity ----- 2 \ i 28 (1528756147779387697 t - 26802077859365356082 t + 1) ) c(i) t = -------------------------------------------------------- / 2 ----- (t - 1) (t - 108819844766059504898 t + 1) i = 0 In Maple notation, these generating functions are (128642502971265742339*t^2+742963079133429834010*t-29)/(t-1)/(t^2-\ 108819844766059504898*t+1) -2*(61220503655255586097*t^2+292606000306947971278*t+1)/(t-1)/(t^2-\ 108819844766059504898*t+1) 28*(1528756147779387697*t^2-26802077859365356082*t+1)/(t-1)/(t^2-\ 108819844766059504898*t+1) Then for all i>=0 we have 3 3 3 52 a(i) + 63 b(i) + 63 c(i) = -114244 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 588, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 16 ( / ----- i = 0 2 87411167948515561041167727131287679704260565112655941681 t / + 175241569552859707280082939416854186891496308203338278832 t - 1) / ( / (t - 1) 2 (t - 761185531995833369397866271340827363191652953181467304962 t + 1)) infinity ----- \ i ) b(i) t = - ( / ----- i = 0 2 1783416287597807289521733427074538867345522325872918680511 t / - 851898905969942744594582341924955840631426588239433652174 t + 15) / ( / (t - 1) 2 (t - 761185531995833369397866271340827363191652953181467304962 t + 1)) infinity ----- \ i ) c(i) t = ( / ----- i = 0 2 1576219445053177811498224740541116219157645430791067559491 t / - 2507736826681042356425375825690699245871741168424552587862 t + 19) / ( / (t - 1) 2 (t - 761185531995833369397866271340827363191652953181467304962 t + 1)) In Maple notation, these generating functions are 16*(87411167948515561041167727131287679704260565112655941681*t^2+ 175241569552859707280082939416854186891496308203338278832*t-1)/(t-1)/(t^2-\ 761185531995833369397866271340827363191652953181467304962*t+1) -(1783416287597807289521733427074538867345522325872918680511*t^2-\ 851898905969942744594582341924955840631426588239433652174*t+15)/(t-1)/(t^2-\ 761185531995833369397866271340827363191652953181467304962*t+1) (1576219445053177811498224740541116219157645430791067559491*t^2-\ 2507736826681042356425375825690699245871741168424552587862*t+19)/(t-1)/(t^2-\ 761185531995833369397866271340827363191652953181467304962*t+1) Then for all i>=0 we have 3 3 3 52 a(i) + 81 b(i) + 81 c(i) = -69212 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 589, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (107807591469687576810770707782126533977 t / ----- i = 0 / + 131548151031815061166836114166129956046 t - 23) / ((t - 1) / 2 (t - 20549021078458662474539711597684580002 t + 1)) infinity ----- \ i 2 ) b(i) t = - 9 (12266096257060774911183033682219314901 t / ----- i = 0 / + 3099108325774629809205421364387735098 t + 1) / ((t - 1) / 2 (t - 20549021078458662474539711597684580002 t + 1)) infinity ----- \ i 2 ) c(i) t = 27 (2491549249098960869494037778782341501 t / ----- i = 0 / - 7613284110044095776290189460984691502 t + 1) / ((t - 1) / 2 (t - 20549021078458662474539711597684580002 t + 1)) In Maple notation, these generating functions are (107807591469687576810770707782126533977*t^2+ 131548151031815061166836114166129956046*t-23)/(t-1)/(t^2-\ 20549021078458662474539711597684580002*t+1) -9*(12266096257060774911183033682219314901*t^2+ 3099108325774629809205421364387735098*t+1)/(t-1)/(t^2-\ 20549021078458662474539711597684580002*t+1) 27*(2491549249098960869494037778782341501*t^2-\ 7613284110044095776290189460984691502*t+1)/(t-1)/(t^2-\ 20549021078458662474539711597684580002*t+1) Then for all i>=0 we have 3 3 3 54 a(i) + 65 b(i) + 65 c(i) = -574992 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 590, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (8044738214454437415066246135217 t / ----- i = 0 / + 10592487833890690183288914307846 t - 23) / ((t - 1) / 2 (t - 1859018893886989033805871279362 t + 1)) infinity ----- \ i ) b(i) t = - 27 / ----- i = 0 2 (434046646353299725502823940561 t - 289815111660573864328476173042 t + 1) / 2 / ((t - 1) (t - 1859018893886989033805871279362 t + 1)) / infinity ----- \ i ) c(i) t = 3 ( / ----- i = 0 2 3532245946739956254406055179691 t - 4830329758974489004975185087382 t + 11 / 2 ) / ((t - 1) (t - 1859018893886989033805871279362 t + 1)) / In Maple notation, these generating functions are (8044738214454437415066246135217*t^2+10592487833890690183288914307846*t-23)/(t-\ 1)/(t^2-1859018893886989033805871279362*t+1) -27*(434046646353299725502823940561*t^2-289815111660573864328476173042*t+1)/(t-\ 1)/(t^2-1859018893886989033805871279362*t+1) 3*(3532245946739956254406055179691*t^2-4830329758974489004975185087382*t+11)/(t -1)/(t^2-1859018893886989033805871279362*t+1) Then for all i>=0 we have 3 3 3 54 a(i) + 67 b(i) + 67 c(i) = -432000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 591, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 5969641744306542433 t + 33179381957626410790 t - 23 ) a(i) t = ---------------------------------------------------- / 2 ----- (t - 1) (t - 6611835114104232098 t + 1) i = 0 infinity ----- 2 \ i 3 (1807135099032483109 t + 7762626250328905450 t + 1) ) b(i) t = - ------------------------------------------------------ / 2 ----- (t - 1) (t - 6611835114104232098 t + 1) i = 0 infinity ----- 2 \ i 21 (103106527282392589 t - 1470215291476876670 t + 1) ) c(i) t = ------------------------------------------------------ / 2 ----- (t - 1) (t - 6611835114104232098 t + 1) i = 0 In Maple notation, these generating functions are (5969641744306542433*t^2+33179381957626410790*t-23)/(t-1)/(t^2-\ 6611835114104232098*t+1) -3*(1807135099032483109*t^2+7762626250328905450*t+1)/(t-1)/(t^2-\ 6611835114104232098*t+1) 21*(103106527282392589*t^2-1470215291476876670*t+1)/(t-1)/(t^2-\ 6611835114104232098*t+1) Then for all i>=0 we have 3 3 3 54 a(i) + 77 b(i) + 77 c(i) = -54000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 592, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 247876177 t + 271756102 t - 23 ) a(i) t = ------------------------------- / 2 ----- (t - 1) (t - 47141954 t + 1) i = 0 infinity ----- 2 \ i 6 (63363789 t - 46066514 t + 5) ) b(i) t = - -------------------------------- / 2 ----- (t - 1) (t - 47141954 t + 1) i = 0 infinity ----- 2 \ i 12 (28927715 t - 37576358 t + 3) ) c(i) t = --------------------------------- / 2 ----- (t - 1) (t - 47141954 t + 1) i = 0 In Maple notation, these generating functions are (247876177*t^2+271756102*t-23)/(t-1)/(t^2-47141954*t+1) -6*(63363789*t^2-46066514*t+5)/(t-1)/(t^2-47141954*t+1) 12*(28927715*t^2-37576358*t+3)/(t-1)/(t^2-47141954*t+1) Then for all i>=0 we have 3 3 3 56 a(i) + 65 b(i) + 65 c(i) = -596288 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 593, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 24 ( / ----- i = 0 2 170687048414393669053792342104071223133254407299698909212005925458724 t + 3320481638015694746343379659628151015684489611263304659797730273886277 t / 2 - 1) / ((t - 1) (t - / 55198950569697775890689144720301592563354566844681190287964962899880002 t + 1)) infinity ----- \ i ) b(i) t = - 20 ( / ----- i = 0 2 230927025074478739395437781003233425859987210549107550395770813278941 t + 1154544642611162647502337564566089415371621439337312763604943394965058 t / 2 + 1) / ((t - 1) (t - / 55198950569697775890689144720301592563354566844681190287964962899880002 t + 1)) infinity ----- \ i ) c(i) t = 26 ( / ----- i = 0 2 142623445254338790498276787006780333095732847642965006107104538325601 t - 1208370881935601395804257822060105595581585655247903709184577006205602 t / 2 + 1) / ((t - 1) (t - / 55198950569697775890689144720301592563354566844681190287964962899880002 t + 1)) In Maple notation, these generating functions are 24*(170687048414393669053792342104071223133254407299698909212005925458724*t^2+ 3320481638015694746343379659628151015684489611263304659797730273886277*t-1)/(t-\ 1)/(t^2-55198950569697775890689144720301592563354566844681190287964962899880002 *t+1) -20*(230927025074478739395437781003233425859987210549107550395770813278941*t^2+ 1154544642611162647502337564566089415371621439337312763604943394965058*t+1)/(t-\ 1)/(t^2-55198950569697775890689144720301592563354566844681190287964962899880002 *t+1) 26*(142623445254338790498276787006780333095732847642965006107104538325601*t^2-\ 1208370881935601395804257822060105595581585655247903709184577006205602*t+1)/(t-\ 1)/(t^2-55198950569697775890689144720301592563354566844681190287964962899880002 *t+1) Then for all i>=0 we have 3 3 3 56 a(i) + 81 b(i) + 81 c(i) = -1512 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 594, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 2 / ----- i = 0 2 (5008581648509606171814356987 t + 721801260735713288881547643026 t - 13) / 2 / ((t - 1) (t - 2046178027603990570787172000002 t + 1)) / infinity ----- \ i ) b(i) t = - 4 / ----- i = 0 2 (2121584698262252295983943001 t + 289528224666107444445174056998 t + 1) / 2 / ((t - 1) (t - 2046178027603990570787172000002 t + 1)) / infinity ----- \ i ) c(i) t = 2 / ----- i = 0 2 (904114964184767144091648011 t - 584203733692924160626407648022 t + 11) / 2 / ((t - 1) (t - 2046178027603990570787172000002 t + 1)) / In Maple notation, these generating functions are 2*(5008581648509606171814356987*t^2+721801260735713288881547643026*t-13)/(t-1)/ (t^2-2046178027603990570787172000002*t+1) -4*(2121584698262252295983943001*t^2+289528224666107444445174056998*t+1)/(t-1)/ (t^2-2046178027603990570787172000002*t+1) 2*(904114964184767144091648011*t^2-584203733692924160626407648022*t+11)/(t-1)/( t^2-2046178027603990570787172000002*t+1) Then for all i>=0 we have 3 3 3 56 a(i) + 93 b(i) + 93 c(i) = -56 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 595, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 8 (469753295342737943419778617749965770062300654944 t / ----- i = 0 / + 707988314446616574816221915573895644655494607449 t - 1) / ((t - 1) / 2 (t - 2484063604387302909543062681203405724886778393154 t + 1)) infinity ----- \ i 2 ) b(i) t = - 2 (1674763153172491466923580499491682877816946659969 t / ----- i = 0 / + 1006274657730104184345363804009790261378034425150 t + 1) / ((t - 1) / 2 (t - 2484063604387302909543062681203405724886778393154 t + 1)) infinity ----- \ i 2 ) c(i) t = 8 (230789470156027689362983677772934411429316403015 t / ----- i = 0 / - 901048922881676602180219753648302696228061674296 t + 1) / ((t - 1) / 2 (t - 2484063604387302909543062681203405724886778393154 t + 1)) In Maple notation, these generating functions are 8*(469753295342737943419778617749965770062300654944*t^2+ 707988314446616574816221915573895644655494607449*t-1)/(t-1)/(t^2-\ 2484063604387302909543062681203405724886778393154*t+1) -2*(1674763153172491466923580499491682877816946659969*t^2+ 1006274657730104184345363804009790261378034425150*t+1)/(t-1)/(t^2-\ 2484063604387302909543062681203405724886778393154*t+1) 8*(230789470156027689362983677772934411429316403015*t^2-\ 901048922881676602180219753648302696228061674296*t+1)/(t-1)/(t^2-\ 2484063604387302909543062681203405724886778393154*t+1) Then for all i>=0 we have 3 3 3 56 a(i) + 95 b(i) + 95 c(i) = -19208 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 596, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = ( / ----- i = 0 2 33843670084581697118410090884812271465412131488151646428648617264235821 t + 360342233856807197255787864922512207496008841518814833126667279724073638 t / 2 - 19) / ((t - 1) (t - / 134571018566093489620194468296760320612207159969145656162388810754317122 t + 1)) infinity ----- \ i ) b(i) t = - 4 ( / ----- i = 0 2 7220230326541738649037405787923404419506993047365300795519881788345881 t + 59469831971699282755660737792771975706896555255928121727433865134147558 t / 2 + 1) / ((t - 1) (t - / 134571018566093489620194468296760320612207159969145656162388810754317122 t + 1)) infinity ----- \ i ) c(i) t = 16 ( / ----- i = 0 2 747442891492256627309036106830467621582619152836586247984701157579101 t - 17419958466052511978483572002004312653183506228659941878723137888202462 t / 2 + 1) / ((t - 1) (t - / 134571018566093489620194468296760320612207159969145656162388810754317122 t + 1)) In Maple notation, these generating functions are (33843670084581697118410090884812271465412131488151646428648617264235821*t^2+ 360342233856807197255787864922512207496008841518814833126667279724073638*t-19)/ (t-1)/(t^2-\ 134571018566093489620194468296760320612207159969145656162388810754317122*t+1) -4*(7220230326541738649037405787923404419506993047365300795519881788345881*t^2+ 59469831971699282755660737792771975706896555255928121727433865134147558*t+1)/(t -1)/(t^2-\ 134571018566093489620194468296760320612207159969145656162388810754317122*t+1) 16*(747442891492256627309036106830467621582619152836586247984701157579101*t^2-\ 17419958466052511978483572002004312653183506228659941878723137888202462*t+1)/(t -1)/(t^2-\ 134571018566093489620194468296760320612207159969145656162388810754317122*t+1) Then for all i>=0 we have 3 3 3 56 a(i) + 97 b(i) + 97 c(i) = -7000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 597, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 2 (1130538827388154724978967479234683463 t / ----- i = 0 / + 10430370748222636422890852322940653350 t - 13) / ((t - 1) / 2 (t - 5979707330721452527359025689383224898 t + 1)) infinity ----- \ i 2 ) b(i) t = - 8 (245169353363167803935186911374229407 t / ----- i = 0 / + 1477779105969795263908637846240288528 t + 1) / ((t - 1) / 2 (t - 5979707330721452527359025689383224898 t + 1)) infinity ----- \ i 2 ) c(i) t = 22 (45550443692848440687986577388740257 t / ----- i = 0 / - 672077156177562283540286489248564962 t + 1) / ((t - 1) / 2 (t - 5979707330721452527359025689383224898 t + 1)) In Maple notation, these generating functions are 2*(1130538827388154724978967479234683463*t^2+ 10430370748222636422890852322940653350*t-13)/(t-1)/(t^2-\ 5979707330721452527359025689383224898*t+1) -8*(245169353363167803935186911374229407*t^2+ 1477779105969795263908637846240288528*t+1)/(t-1)/(t^2-\ 5979707330721452527359025689383224898*t+1) 22*(45550443692848440687986577388740257*t^2-\ 672077156177562283540286489248564962*t+1)/(t-1)/(t^2-\ 5979707330721452527359025689383224898*t+1) Then for all i>=0 we have 3 3 3 56 a(i) + 99 b(i) + 99 c(i) = -19208 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 598, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 3 (257014039856136988671993 t + 316315515561567338086414 t - 7) ---------------------------------------------------------------- 2 (t - 1) (t - 179898809414277346099202 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 3 (346790971707954917703687 t - 175522103537142165831694 t + 7) - ---------------------------------------------------------------- 2 (t - 1) (t - 179898809414277346099202 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 886164491210182559907869 t - 1399971095722620815523898 t + 29 -------------------------------------------------------------- 2 (t - 1) (t - 179898809414277346099202 t + 1) In Maple notation, these generating functions are 3*(257014039856136988671993*t^2+316315515561567338086414*t-7)/(t-1)/(t^2-\ 179898809414277346099202*t+1) -3*(346790971707954917703687*t^2-175522103537142165831694*t+7)/(t-1)/(t^2-\ 179898809414277346099202*t+1) (886164491210182559907869*t^2-1399971095722620815523898*t+29)/(t-1)/(t^2-\ 179898809414277346099202*t+1) Then for all i>=0 we have 3 3 3 61 a(i) + 65 b(i) + 65 c(i) = -418399 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 599, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 2 (3978891325689995564921 t + 49219797490143329462414 t - 7) ------------------------------------------------------------- 2 (t - 1) (t - 40489660553551550595074 t + 1) infinity ----- 2 \ i 7387231500586465583617 t + 82064775114704485228030 t + 1 ) b(i) t = - --------------------------------------------------------- / 2 ----- (t - 1) (t - 40489660553551550595074 t + 1) i = 0 infinity ----- 2 \ i 2082043066333138163725 t - 91534049681624088975386 t + 13 ) c(i) t = ---------------------------------------------------------- / 2 ----- (t - 1) (t - 40489660553551550595074 t + 1) i = 0 In Maple notation, these generating functions are 2*(3978891325689995564921*t^2+49219797490143329462414*t-7)/(t-1)/(t^2-\ 40489660553551550595074*t+1) -(7387231500586465583617*t^2+82064775114704485228030*t+1)/(t-1)/(t^2-\ 40489660553551550595074*t+1) (2082043066333138163725*t^2-91534049681624088975386*t+13)/(t-1)/(t^2-\ 40489660553551550595074*t+1) Then for all i>=0 we have 3 3 3 61 a(i) + 78 b(i) + 78 c(i) = -3904 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 600, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 21 (26670581736828233497623791 t + 27307425660169287750440402 t - 1) --------------------------------------------------------------------- 2 (t - 1) (t - 106686128474170238772313922 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 16 (38127440152819306382715469 t - 15534046045936340129849798 t + 1) - --------------------------------------------------------------------- 2 (t - 1) (t - 106686128474170238772313922 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 490021424629381851384140449 t - 851515730339509311429991226 t + 25 ------------------------------------------------------------------- 2 (t - 1) (t - 106686128474170238772313922 t + 1) In Maple notation, these generating functions are 21*(26670581736828233497623791*t^2+27307425660169287750440402*t-1)/(t-1)/(t^2-\ 106686128474170238772313922*t+1) -16*(38127440152819306382715469*t^2-15534046045936340129849798*t+1)/(t-1)/(t^2-\ 106686128474170238772313922*t+1) (490021424629381851384140449*t^2-851515730339509311429991226*t+25)/(t-1)/(t^2-\ 106686128474170238772313922*t+1) Then for all i>=0 we have 3 3 3 61 a(i) + 98 b(i) + 98 c(i) = -564921 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 601, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 9 (1702769287155630046079 t + 3288643549082903822722 t - 1) ) a(i) t = ------------------------------------------------------------ / 2 ----- (t - 1) (t - 11617003327077219052802 t + 1) i = 0 infinity ----- \ i ) b(i) t = / ----- i = 0 2 2 (7831522723988269946641 t + 7948694627972647326958 t + 1) - ------------------------------------------------------------ 2 (t - 1) (t - 11617003327077219052802 t + 1) infinity ----- 2 \ i 10 (800058365577620468593 t - 3956101835969803923314 t + 1) ) c(i) t = ------------------------------------------------------------ / 2 ----- (t - 1) (t - 11617003327077219052802 t + 1) i = 0 In Maple notation, these generating functions are 9*(1702769287155630046079*t^2+3288643549082903822722*t-1)/(t-1)/(t^2-\ 11617003327077219052802*t+1) -2*(7831522723988269946641*t^2+7948694627972647326958*t+1)/(t-1)/(t^2-\ 11617003327077219052802*t+1) 10*(800058365577620468593*t^2-3956101835969803923314*t+1)/(t-1)/(t^2-\ 11617003327077219052802*t+1) Then for all i>=0 we have 3 3 3 62 a(i) + 67 b(i) + 67 c(i) = -21266 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 602, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 56136869222313537982354783 t + 63951644258111684366653234 t - 17 ----------------------------------------------------------------- 2 (t - 1) (t - 14927337133821780626649602 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 73245179079532388207409857 t - 40615551113934777991464274 t + 17 - ----------------------------------------------------------------- 2 (t - 1) (t - 14927337133821780626649602 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 63038475584566290392436263 t - 95668103550163900608381886 t + 23 ----------------------------------------------------------------- 2 (t - 1) (t - 14927337133821780626649602 t + 1) In Maple notation, these generating functions are (56136869222313537982354783*t^2+63951644258111684366653234*t-17)/(t-1)/(t^2-\ 14927337133821780626649602*t+1) -(73245179079532388207409857*t^2-40615551113934777991464274*t+17)/(t-1)/(t^2-\ 14927337133821780626649602*t+1) (63038475584566290392436263*t^2-95668103550163900608381886*t+23)/(t-1)/(t^2-\ 14927337133821780626649602*t+1) Then for all i>=0 we have 3 3 3 62 a(i) + 77 b(i) + 77 c(i) = -253952 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 603, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 27 (379062512903703177508938440248548764584559 t / ----- i = 0 / + 3884554340913840691240655265056556356666642 t - 1) / ((t - 1) / 2 (t - 19359125174090469458106263310574531361356802 t + 1)) infinity ----- \ i 2 ) b(i) t = - (9428993459075794418748142694312857319984761 t / ----- i = 0 / + 87020933747553508774316990585156682855346438 t + 1) / ((t - 1) / 2 (t - 19359125174090469458106263310574531361356802 t + 1)) infinity ----- \ i 2 ) c(i) t = 5 (521173645361827444717450153967795911492541 t / ----- i = 0 / - 19811159086687688083330476809861703946558786 t + 5) / ((t - 1) / 2 (t - 19359125174090469458106263310574531361356802 t + 1)) In Maple notation, these generating functions are 27*(379062512903703177508938440248548764584559*t^2+ 3884554340913840691240655265056556356666642*t-1)/(t-1)/(t^2-\ 19359125174090469458106263310574531361356802*t+1) -(9428993459075794418748142694312857319984761*t^2+ 87020933747553508774316990585156682855346438*t+1)/(t-1)/(t^2-\ 19359125174090469458106263310574531361356802*t+1) 5*(521173645361827444717450153967795911492541*t^2-\ 19811159086687688083330476809861703946558786*t+5)/(t-1)/(t^2-\ 19359125174090469458106263310574531361356802*t+1) Then for all i>=0 we have 3 3 3 62 a(i) + 81 b(i) + 81 c(i) = -45198 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 604, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 8966583487243393220647 t + 740548730613027791505994 t - 17 ) a(i) t = ----------------------------------------------------------- / 2 ----- (t - 1) (t - 1097425759212565856341634 t + 1) i = 0 infinity ----- \ i ) b(i) t = / ----- i = 0 2 3 (2643207333623416505485 t + 202572467478914032502098 t + 1) - -------------------------------------------------------------- 2 (t - 1) (t - 1097425759212565856341634 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 3 (650633225347106900897 t - 205866308037884555908486 t + 5) ------------------------------------------------------------- 2 (t - 1) (t - 1097425759212565856341634 t + 1) In Maple notation, these generating functions are (8966583487243393220647*t^2+740548730613027791505994*t-17)/(t-1)/(t^2-\ 1097425759212565856341634*t+1) -3*(2643207333623416505485*t^2+202572467478914032502098*t+1)/(t-1)/(t^2-\ 1097425759212565856341634*t+1) 3*(650633225347106900897*t^2-205866308037884555908486*t+5)/(t-1)/(t^2-\ 1097425759212565856341634*t+1) Then for all i>=0 we have 3 3 3 62 a(i) + 91 b(i) + 91 c(i) = -62 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 605, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 24 (44779299555613347223839 t + 86717643943487358184162 t - 1) --------------------------------------------------------------- 2 (t - 1) (t - 267400359336029175705602 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 983514331845063670256161 t + 1335740349254663723535838 t + 1 - ------------------------------------------------------------- 2 (t - 1) (t - 267400359336029175705602 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 25 (15892503688317739536673 t - 108662690932306835288354 t + 1) ---------------------------------------------------------------- 2 (t - 1) (t - 267400359336029175705602 t + 1) In Maple notation, these generating functions are 24*(44779299555613347223839*t^2+86717643943487358184162*t-1)/(t-1)/(t^2-\ 267400359336029175705602*t+1) -(983514331845063670256161*t^2+1335740349254663723535838*t+1)/(t-1)/(t^2-\ 267400359336029175705602*t+1) 25*(15892503688317739536673*t^2-108662690932306835288354*t+1)/(t-1)/(t^2-\ 267400359336029175705602*t+1) Then for all i>=0 we have 3 3 3 63 a(i) + 88 b(i) + 88 c(i) = -504000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 606, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (28869708517780821870815097184416355183 t / ----- i = 0 / + 35357884874193786289260785374006684834 t - 17) / ((t - 1) / 2 (t - 7689900112442742995069326300293120002 t + 1)) infinity ----- \ i 2 ) b(i) t = - 8 (3783211703293084775398849789112860801 t / ----- i = 0 / + 472833641958244680991720741866979198 t + 1) / ((t - 1) / 2 (t - 7689900112442742995069326300293120002 t + 1)) infinity ----- \ i 2 ) c(i) t = 20 (988380890084855330690174512292119681 t / ----- i = 0 / - 2690799028185387113246402724684055682 t + 1) / ((t - 1) / 2 (t - 7689900112442742995069326300293120002 t + 1)) In Maple notation, these generating functions are (28869708517780821870815097184416355183*t^2+ 35357884874193786289260785374006684834*t-17)/(t-1)/(t^2-\ 7689900112442742995069326300293120002*t+1) -8*(3783211703293084775398849789112860801*t^2+ 472833641958244680991720741866979198*t+1)/(t-1)/(t^2-\ 7689900112442742995069326300293120002*t+1) 20*(988380890084855330690174512292119681*t^2-\ 2690799028185387113246402724684055682*t+1)/(t-1)/(t^2-\ 7689900112442742995069326300293120002*t+1) Then for all i>=0 we have 3 3 3 64 a(i) + 77 b(i) + 77 c(i) = -262144 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 607, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 3 (35519545217 t + 294250381574 t - 7) ) a(i) t = --------------------------------------- / 2 ----- (t - 1) (t - 303735458882 t + 1) i = 0 infinity ----- 2 \ i 8 (13070157409 t + 65033246302 t + 1) ) b(i) t = - -------------------------------------- / 2 ----- (t - 1) (t - 303735458882 t + 1) i = 0 infinity ----- 2 \ i 4 (14300466413 t - 170507273842 t + 5) ) c(i) t = --------------------------------------- / 2 ----- (t - 1) (t - 303735458882 t + 1) i = 0 In Maple notation, these generating functions are 3*(35519545217*t^2+294250381574*t-7)/(t-1)/(t^2-303735458882*t+1) -8*(13070157409*t^2+65033246302*t+1)/(t-1)/(t^2-303735458882*t+1) 4*(14300466413*t^2-170507273842*t+5)/(t-1)/(t^2-303735458882*t+1) Then for all i>=0 we have 3 3 3 64 a(i) + 81 b(i) + 81 c(i) = -13824 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 608, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (87708788801677232472178399667448431989534327957933219 t / ----- i = 0 / + 518347122688796309890678735645527950934167885346591610 t - 29) / ( / 2 (t - 1) (t - 117522146315109217345145340151994550775639646579920898 t + 1) ) infinity ----- \ i ) b(i) t = - 16 ( / ----- i = 0 2 5603422057158289318276009729934204146818788204579809 t / + 11524245006702919487630822354997737109720622171417630 t + 1) / ( / 2 (t - 1) (t - 117522146315109217345145340151994550775639646579920898 t + 1) ) infinity ----- \ i 2 ) c(i) t = 4 (15666858320811831698321085099163860280387896821555143 t / ----- i = 0 / - 84177526576256666921948413438891625306545538325544910 t + 7) / ( / 2 (t - 1) (t - 117522146315109217345145340151994550775639646579920898 t + 1) ) In Maple notation, these generating functions are (87708788801677232472178399667448431989534327957933219*t^2+ 518347122688796309890678735645527950934167885346591610*t-29)/(t-1)/(t^2-\ 117522146315109217345145340151994550775639646579920898*t+1) -16*(5603422057158289318276009729934204146818788204579809*t^2+ 11524245006702919487630822354997737109720622171417630*t+1)/(t-1)/(t^2-\ 117522146315109217345145340151994550775639646579920898*t+1) 4*(15666858320811831698321085099163860280387896821555143*t^2-\ 84177526576256666921948413438891625306545538325544910*t+7)/(t-1)/(t^2-\ 117522146315109217345145340151994550775639646579920898*t+1) Then for all i>=0 we have 3 3 3 64 a(i) + 91 b(i) + 91 c(i) = -64000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 609, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (2252113761860627692799702590314105357897730309281571 t / ----- i = 0 / + 28962420677853729930917794879880610053005551773841658 t - 29) / ( / 2 (t - 1) (t - 9371498578927636281018092183962412108010492072652802 t + 1)) infinity ----- \ i 2 ) b(i) t = - 10 (206499072567114176105687915772774864353851819576705 t / ----- i = 0 / + 1792210091165004116690336097346520862708233540858494 t + 1) / ((t - 1) / 2 (t - 9371498578927636281018092183962412108010492072652802 t + 1)) infinity ----- \ i 2 ) c(i) t = 2 (517726502981713122174221843934935954249777884333453 t / ----- i = 0 / - 10511272321642304586154341909531414589560204686509466 t + 13) / ( / 2 (t - 1) (t - 9371498578927636281018092183962412108010492072652802 t + 1)) In Maple notation, these generating functions are (2252113761860627692799702590314105357897730309281571*t^2+ 28962420677853729930917794879880610053005551773841658*t-29)/(t-1)/(t^2-\ 9371498578927636281018092183962412108010492072652802*t+1) -10*(206499072567114176105687915772774864353851819576705*t^2+ 1792210091165004116690336097346520862708233540858494*t+1)/(t-1)/(t^2-\ 9371498578927636281018092183962412108010492072652802*t+1) 2*(517726502981713122174221843934935954249777884333453*t^2-\ 10511272321642304586154341909531414589560204686509466*t+13)/(t-1)/(t^2-\ 9371498578927636281018092183962412108010492072652802*t+1) Then for all i>=0 we have 3 3 3 64 a(i) + 95 b(i) + 95 c(i) = -13824 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 610, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 5 / ----- i = 0 2 (245335384681349830387344773779 t + 1919548978186027218634759436914 t - 5) / 2 / ((t - 1) (t - 2377262259224619734210981522498 t + 1)) / infinity ----- \ i ) b(i) t = - 2 / ----- i = 0 2 (548467469203579588141981280699 t + 3068807668752037759591154868802 t + 3) / 2 / ((t - 1) (t - 2377262259224619734210981522498 t + 1)) / infinity ----- \ i ) c(i) t = 2 ( / ----- i = 0 2 251091245347397975551260342787 t - 3868366383303015323284396492302 t + 11) / 2 / ((t - 1) (t - 2377262259224619734210981522498 t + 1)) / In Maple notation, these generating functions are 5*(245335384681349830387344773779*t^2+1919548978186027218634759436914*t-5)/(t-1 )/(t^2-2377262259224619734210981522498*t+1) -2*(548467469203579588141981280699*t^2+3068807668752037759591154868802*t+3)/(t-\ 1)/(t^2-2377262259224619734210981522498*t+1) 2*(251091245347397975551260342787*t^2-3868366383303015323284396492302*t+11)/(t-\ 1)/(t^2-2377262259224619734210981522498*t+1) Then for all i>=0 we have 3 3 3 64 a(i) + 99 b(i) + 99 c(i) = -32768 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 611, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (1080015905752017010525905755117171 t / ----- i = 0 / + 1510096870773709412767705542337178 t - 13) / ((t - 1) / 2 (t - 467409591777406082040717468087554 t + 1)) infinity ----- \ i 2 ) b(i) t = - 4 (352223272895352973925920891628731 t / ----- i = 0 / - 150879046695426064401402572711614 t + 3) / ((t - 1) / 2 (t - 467409591777406082040717468087554 t + 1)) infinity ----- \ i 2 ) c(i) t = (1183889777883075018510786534198849 t / ----- i = 0 / - 1989266682682782656608859809867346 t + 17) / ((t - 1) / 2 (t - 467409591777406082040717468087554 t + 1)) In Maple notation, these generating functions are (1080015905752017010525905755117171*t^2+1510096870773709412767705542337178*t-13 )/(t-1)/(t^2-467409591777406082040717468087554*t+1) -4*(352223272895352973925920891628731*t^2-150879046695426064401402572711614*t+3 )/(t-1)/(t^2-467409591777406082040717468087554*t+1) (1183889777883075018510786534198849*t^2-1989266682682782656608859809867346*t+17 )/(t-1)/(t^2-467409591777406082040717468087554*t+1) Then for all i>=0 we have 3 3 3 65 a(i) + 72 b(i) + 72 c(i) = -86515 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 612, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 16 (129684407697807243808269479654147034089 t / ----- i = 0 / + 661841381404792821974936386765067854712 t - 1) / ((t - 1) / 2 (t - 4171548088137071049942900170166483513602 t + 1)) infinity ----- \ i 2 ) b(i) t = - 12 (199264334790195621904689752640842391781 t / ----- i = 0 / + 157683592808895546203157736788194912218 t + 1) / ((t - 1) / 2 (t - 4171548088137071049942900170166483513602 t + 1)) infinity ----- \ i 2 ) c(i) t = (1919592353126684758098933469311392213777 t / ----- i = 0 / - 6202967484315778775393103342459839861794 t + 17) / ((t - 1) / 2 (t - 4171548088137071049942900170166483513602 t + 1)) In Maple notation, these generating functions are 16*(129684407697807243808269479654147034089*t^2+ 661841381404792821974936386765067854712*t-1)/(t-1)/(t^2-\ 4171548088137071049942900170166483513602*t+1) -12*(199264334790195621904689752640842391781*t^2+ 157683592808895546203157736788194912218*t+1)/(t-1)/(t^2-\ 4171548088137071049942900170166483513602*t+1) (1919592353126684758098933469311392213777*t^2-\ 6202967484315778775393103342459839861794*t+17)/(t-1)/(t^2-\ 4171548088137071049942900170166483513602*t+1) Then for all i>=0 we have 3 3 3 65 a(i) + 88 b(i) + 88 c(i) = -14040 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 613, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 18 (1126142471425178081478687 t + 11036046809083465592458786 t - 1) -------------------------------------------------------------------- 2 (t - 1) (t - 56253221702719205261735234 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 17953652894366171139596377 t + 155933452501093459392055462 t + 1 - ----------------------------------------------------------------- 2 (t - 1) (t - 56253221702719205261735234 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 16 (330284380677057357685072 t - 11198228467893284265913313 t + 1) ------------------------------------------------------------------- 2 (t - 1) (t - 56253221702719205261735234 t + 1) In Maple notation, these generating functions are 18*(1126142471425178081478687*t^2+11036046809083465592458786*t-1)/(t-1)/(t^2-\ 56253221702719205261735234*t+1) -(17953652894366171139596377*t^2+155933452501093459392055462*t+1)/(t-1)/(t^2-\ 56253221702719205261735234*t+1) 16*(330284380677057357685072*t^2-11198228467893284265913313*t+1)/(t-1)/(t^2-\ 56253221702719205261735234*t+1) Then for all i>=0 we have 3 3 3 65 a(i) + 96 b(i) + 96 c(i) = -14040 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 614, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 19 ( / ----- i = 0 2 966428577649233458405358319825268429478317987428292943617999 t + 2554027831074886722618665029027384740214988845410099152502002 t - 1) / / ((t - 1) / 2 (t - 12152052066559271535177393723294978817959835292774749616520002 t + 1) ) infinity ----- \ i ) b(i) t = - 4 ( / ----- i = 0 2 8428026812633690155784148716559641148802218077580134345673007 t - 5921011256409811776704051534254076433530580352024488150573014 t + 7) / / ((t - 1) / 2 (t - 12152052066559271535177393723294978817959835292774749616520002 t + 1) ) infinity ----- \ i ) c(i) t = ( / ----- i = 0 2 31875892953001217052166414058570554579200068134206780789817831 t - 41903955177896730568486802787792813440286619036429365570217862 t + 31) / / ((t - 1) / 2 (t - 12152052066559271535177393723294978817959835292774749616520002 t + 1) ) In Maple notation, these generating functions are 19*(966428577649233458405358319825268429478317987428292943617999*t^2+ 2554027831074886722618665029027384740214988845410099152502002*t-1)/(t-1)/(t^2-\ 12152052066559271535177393723294978817959835292774749616520002*t+1) -4*(8428026812633690155784148716559641148802218077580134345673007*t^2-\ 5921011256409811776704051534254076433530580352024488150573014*t+7)/(t-1)/(t^2-\ 12152052066559271535177393723294978817959835292774749616520002*t+1) (31875892953001217052166414058570554579200068134206780789817831*t^2-\ 41903955177896730568486802787792813440286619036429365570217862*t+31)/(t-1)/(t^2 -12152052066559271535177393723294978817959835292774749616520002*t+1) Then for all i>=0 we have 3 3 3 67 a(i) + 70 b(i) + 70 c(i) = -89177 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 615, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 34482588661 t + 1117592641558 t - 11 ) a(i) t = ------------------------------------- / 2 ----- (t - 1) (t - 2080973583362 t + 1) i = 0 infinity ----- 2 \ i 34944445541 t + 773317757846 t + 5 ) b(i) t = - ----------------------------------- / 2 ----- (t - 1) (t - 2080973583362 t + 1) i = 0 infinity ----- 2 \ i 17703151211 t - 825965354614 t + 11 ) c(i) t = ------------------------------------ / 2 ----- (t - 1) (t - 2080973583362 t + 1) i = 0 In Maple notation, these generating functions are (34482588661*t^2+1117592641558*t-11)/(t-1)/(t^2-2080973583362*t+1) -(34944445541*t^2+773317757846*t+5)/(t-1)/(t^2-2080973583362*t+1) (17703151211*t^2-825965354614*t+11)/(t-1)/(t^2-2080973583362*t+1) Then for all i>=0 we have 3 3 3 67 a(i) + 74 b(i) + 74 c(i) = -67 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 616, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 16 ( / ----- i = 0 112766142522967362581186416376408746203050459645393622991801886848001530799 2 t + 967302332853326007262410286379387658552484448555373741963345867109472274002 / 2 t - 1) / ((t - 1) (t - 8578939619031663557973381296755488020660719342\ / 143706556577786794357403340802 t + 1)) infinity ----- \ i ) b(i) t = - 15 ( / ----- i = 0 153968469941320748621348003210060461989406507483551862712998324199075002657 2 t + 190010557272994905707925812997370835068803065181695497724291750739252958942 / 2 t + 1) / ((t - 1) (t - 8578939619031663557973381296755488020660719342\ / 143706556577786794357403340802 t + 1)) infinity ----- \ i ) c(i) t = (19486753930463156690604235157463989419913361413880183471\ / ----- i = 0 2 21208825072520141299 t - 7108360801261050483999530758857868397864479731\ / 2 366728753680559949147439565318 t + 19) / ((t - 1) (t - 85789396190316\ / 63557973381296755488020660719342143706556577786794357403340802 t + 1)) In Maple notation, these generating functions are 16*(112766142522967362581186416376408746203050459645393622991801886848001530799 *t^2+ 967302332853326007262410286379387658552484448555373741963345867109472274002*t-1 )/(t-1)/(t^2-\ 8578939619031663557973381296755488020660719342143706556577786794357403340802*t+ 1) -15*( 153968469941320748621348003210060461989406507483551862712998324199075002657*t^2 +190010557272994905707925812997370835068803065181695497724291750739252958942*t+ 1)/(t-1)/(t^2-\ 8578939619031663557973381296755488020660719342143706556577786794357403340802*t+ 1) (1948675393046315669060423515746398941991336141388018347121208825072520141299*t ^2-7108360801261050483999530758857868397864479731366728753680559949147439565318 *t+19)/(t-1)/(t^2-\ 8578939619031663557973381296755488020660719342143706556577786794357403340802*t+ 1) Then for all i>=0 we have 3 3 3 67 a(i) + 80 b(i) + 80 c(i) = -4288 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 617, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 2 (2524027 t + 4109962 t - 5) ) a(i) t = ------------------------------ / 2 ----- (t - 1) (t - 3204098 t + 1) i = 0 infinity ----- 2 \ i 5323493 t + 1159958 t + 5 ) b(i) t = - ---------------------------- / 2 ----- (t - 1) (t - 3204098 t + 1) i = 0 infinity ----- 2 \ i 3640811 t - 10124278 t + 11 ) c(i) t = ---------------------------- / 2 ----- (t - 1) (t - 3204098 t + 1) i = 0 In Maple notation, these generating functions are 2*(2524027*t^2+4109962*t-5)/(t-1)/(t^2-3204098*t+1) -(5323493*t^2+1159958*t+5)/(t-1)/(t^2-3204098*t+1) (3640811*t^2-10124278*t+11)/(t-1)/(t^2-3204098*t+1) Then for all i>=0 we have 3 3 3 67 a(i) + 84 b(i) + 84 c(i) = -34304 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 618, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 27 / ----- i = 0 2 (83358529903160142866365770639 t + 3482173702843984584133802664562 t - 1) / 2 / ((t - 1) (t - 31762870204460869398761681644802 t + 1)) / infinity ----- \ i ) b(i) t = - ( / ----- i = 0 2 2084745167014997399364179853841 t + 84362035904733280751881474725358 t + 1 / 2 ) / ((t - 1) (t - 31762870204460869398761681644802 t + 1)) / infinity ----- \ i ) c(i) t = 5 / ----- i = 0 2 (68456598711078366470222942549 t - 17357812813060733996719353858394 t + 5) / 2 / ((t - 1) (t - 31762870204460869398761681644802 t + 1)) / In Maple notation, these generating functions are 27*(83358529903160142866365770639*t^2+3482173702843984584133802664562*t-1)/(t-1 )/(t^2-31762870204460869398761681644802*t+1) -(2084745167014997399364179853841*t^2+84362035904733280751881474725358*t+1)/(t-\ 1)/(t^2-31762870204460869398761681644802*t+1) 5*(68456598711078366470222942549*t^2-17357812813060733996719353858394*t+5)/(t-1 )/(t^2-31762870204460869398761681644802*t+1) Then for all i>=0 we have 3 3 3 72 a(i) + 91 b(i) + 91 c(i) = -4608 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 619, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 2 (257661159517761005222795027 t + 542751106538858649012507386 t - 13) ----------------------------------------------------------------------- 2 (t - 1) (t - 171270726688498276461081602 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 571037098070384148270342013 t + 280544286021653721687853174 t + 13 - ------------------------------------------------------------------- 2 (t - 1) (t - 171270726688498276461081602 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 383647163875648871744672909 t - 1235228547967686741702868138 t + 29 -------------------------------------------------------------------- 2 (t - 1) (t - 171270726688498276461081602 t + 1) In Maple notation, these generating functions are 2*(257661159517761005222795027*t^2+542751106538858649012507386*t-13)/(t-1)/(t^2 -171270726688498276461081602*t+1) -(571037098070384148270342013*t^2+280544286021653721687853174*t+13)/(t-1)/(t^2-\ 171270726688498276461081602*t+1) (383647163875648871744672909*t^2-1235228547967686741702868138*t+29)/(t-1)/(t^2-\ 171270726688498276461081602*t+1) Then for all i>=0 we have 3 3 3 73 a(i) + 77 b(i) + 77 c(i) = -425736 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 620, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 12 (1246274454764933105988394999425388486233806399 t / ----- i = 0 / + 2644462286352487908766893453635176631752178114 t - 1) / ((t - 1) / 2 (t - 11595796408469433171635646928025023043948408834 t + 1)) infinity ----- \ i 2 ) b(i) t = - 11 (1810771296002627201941273763707443734075994625 t / ----- i = 0 / - 542996639992040678758104337699016772554002946 t + 1) / ((t - 1) / 2 (t - 11595796408469433171635646928025023043948408834 t + 1)) infinity ----- \ i 2 ) c(i) t = 3 (5642475188197686588993954467386982902624935173 t / ----- i = 0 / - 10290982260236503840665575696084548428205571338 t + 5) / ((t - 1) / 2 (t - 11595796408469433171635646928025023043948408834 t + 1)) In Maple notation, these generating functions are 12*(1246274454764933105988394999425388486233806399*t^2+ 2644462286352487908766893453635176631752178114*t-1)/(t-1)/(t^2-\ 11595796408469433171635646928025023043948408834*t+1) -11*(1810771296002627201941273763707443734075994625*t^2-\ 542996639992040678758104337699016772554002946*t+1)/(t-1)/(t^2-\ 11595796408469433171635646928025023043948408834*t+1) 3*(5642475188197686588993954467386982902624935173*t^2-\ 10290982260236503840665575696084548428205571338*t+5)/(t-1)/(t^2-\ 11595796408469433171635646928025023043948408834*t+1) Then for all i>=0 we have 3 3 3 73 a(i) + 80 b(i) + 80 c(i) = -37376 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 621, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (1610200180176878154739536890078237 t / ----- i = 0 / + 8386061028098375721048496518579254 t - 19) / ((t - 1) / 2 (t - 2233328173224253268518521052962434 t + 1)) infinity ----- \ i 2 ) b(i) t = - (1627679233734815239460283248310981 t / ----- i = 0 / + 5596032105468331433412065374892662 t + 5) / ((t - 1) / 2 (t - 2233328173224253268518521052962434 t + 1)) infinity ----- \ i 2 ) c(i) t = (792760621791248788854597453455603 t / ----- i = 0 / - 8016471960994395461726946076659270 t + 19) / ((t - 1) / 2 (t - 2233328173224253268518521052962434 t + 1)) In Maple notation, these generating functions are (1610200180176878154739536890078237*t^2+8386061028098375721048496518579254*t-19 )/(t-1)/(t^2-2233328173224253268518521052962434*t+1) -(1627679233734815239460283248310981*t^2+5596032105468331433412065374892662*t+5 )/(t-1)/(t^2-2233328173224253268518521052962434*t+1) (792760621791248788854597453455603*t^2-8016471960994395461726946076659270*t+19) /(t-1)/(t^2-2233328173224253268518521052962434*t+1) Then for all i>=0 we have 3 3 3 74 a(i) + 81 b(i) + 81 c(i) = -37888 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 622, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 18 (50509891751612218158342741968002081953 t / ----- i = 0 / + 721309861880914575701941715401558747012 t - 1) / ((t - 1) / 2 (t - 9061165106402956479663148491675136124834 t + 1)) infinity ----- \ i 2 ) b(i) t = - (1002652163873570370612726600579082808431 t / ----- i = 0 / + 4865383676782765590597925643374846233820 t + 13) / ((t - 1) / 2 (t - 9061165106402956479663148491675136124834 t + 1)) infinity ----- \ i 2 ) c(i) t = (742887006293850391512678213315072101245 t / ----- i = 0 / - 6610922846950186352723330457269001143528 t + 19) / ((t - 1) / 2 (t - 9061165106402956479663148491675136124834 t + 1)) In Maple notation, these generating functions are 18*(50509891751612218158342741968002081953*t^2+ 721309861880914575701941715401558747012*t-1)/(t-1)/(t^2-\ 9061165106402956479663148491675136124834*t+1) -(1002652163873570370612726600579082808431*t^2+ 4865383676782765590597925643374846233820*t+13)/(t-1)/(t^2-\ 9061165106402956479663148491675136124834*t+1) (742887006293850391512678213315072101245*t^2-\ 6610922846950186352723330457269001143528*t+19)/(t-1)/(t^2-\ 9061165106402956479663148491675136124834*t+1) Then for all i>=0 we have 3 3 3 74 a(i) + 93 b(i) + 93 c(i) = -1998 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 623, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 17 ( / ----- i = 0 2 40019246855438602996147205309296489725184461083310426178199 t / + 473849060823783571597156450272959654177471936081550453901802 t - 1) / / ((t - 1) 2 (t - 3788673618031932017002538219367372773939455127984902741320002 t + 1)) infinity ----- \ i ) b(i) t = - 5 ( / ----- i = 0 2 138303330912541073988117520791141388605119407626723246599641 t + 1226865566383144928074529051915592642372193693158547949208358 t + 1) / / ((t - 1) / 2 (t - 3788673618031932017002538219367372773939455127984902741320002 t + 1)) infinity ----- \ i ) c(i) t = 17 ( / ----- i = 0 2 17809309208143803242404229131578044536694419439245417234201 t / - 419329573118639686202006162280617465412374743199619298354202 t + 1) / / ((t - 1) 2 (t - 3788673618031932017002538219367372773939455127984902741320002 t + 1)) In Maple notation, these generating functions are 17*(40019246855438602996147205309296489725184461083310426178199*t^2+ 473849060823783571597156450272959654177471936081550453901802*t-1)/(t-1)/(t^2-\ 3788673618031932017002538219367372773939455127984902741320002*t+1) -5*(138303330912541073988117520791141388605119407626723246599641*t^2+ 1226865566383144928074529051915592642372193693158547949208358*t+1)/(t-1)/(t^2-\ 3788673618031932017002538219367372773939455127984902741320002*t+1) 17*(17809309208143803242404229131578044536694419439245417234201*t^2-\ 419329573118639686202006162280617465412374743199619298354202*t+1)/(t-1)/(t^2-\ 3788673618031932017002538219367372773939455127984902741320002*t+1) Then for all i>=0 we have 3 3 3 76 a(i) + 79 b(i) + 79 c(i) = -4864 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 624, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 2 (124519553822190602098929238704598522339459513949106601\ / ----- i = 0 2 2169198297230934537582909 t + 11914957755338044052125487317969045030073\ / 2 376945779387969030990371179444061417102 t - 11) / ((t - 1) (t - 10500\ / 806424768354540502223356408101112950963066698828837237011083654413228486\ 402 t + 1)) infinity ----- \ i ) b(i) t = - (380135996919029717590895948292055903705247850899815367\ / ----- i = 0 2 9726596836658902564859987 t + 20374799353253822943681276424180014127023\ / 2 92565374813146094546330385010275171986 t + 27) / ((t - 1) (t - 105008\ / 064247683545405022233564081011129509630666988288372370110836544132284864\ 02 t + 1)) infinity ----- \ i ) c(i) t = (34324131430504731696899098867587856375281540232230230094\ / ----- i = 0 2 54241785627514553724311 t - 9271253047566152639966997012097346087283025\ / 2 097595989835275384952671427393756342 t + 31) / ((t - 1) (t - 10500806\ / 424768354540502223356408101112950963066698828837237011083654413228486402 t + 1)) In Maple notation, these generating functions are 2*(1245195538221906020989292387045985223394595139491066012169198297230934537582\ 909*t^2+11914957755338044052125487317969045030073376945779387969030990371179444\ 061417102*t-11)/(t-1)/(t^2-1050080642476835454050222335640810111295096306669882\ 8837237011083654413228486402*t+1) -(38013599691902971759089594829205590370524785089981536797265968366589025648599\ 87*t^2+203747993532538229436812764241800141270239256537481314609454633038501027\ 5171986*t+27)/(t-1)/(t^2-105008064247683545405022233564081011129509630666988288\ 37237011083654413228486402*t+1) (343241314305047316968990988675878563752815402322302300945424178562751455372431\ 1*t^2-9271253047566152639966997012097346087283025097595989835275384952671427393\ 756342*t+31)/(t-1)/(t^2-1050080642476835454050222335640810111295096306669882883\ 7237011083654413228486402*t+1) Then for all i>=0 we have 3 3 3 76 a(i) + 81 b(i) + 81 c(i) = -9500 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 625, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 18 (1115023214533194150193179162539677253619 t / ----- i = 0 / + 20902567364856755819122982741206134454174 t - 1) / ((t - 1) / 2 (t - 223602414174936635551215229139542233209282 t + 1)) infinity ----- \ i 2 ) b(i) t = - (19190443461097430763218924729937754302953 t / ----- i = 0 / + 285702091668567999551448675751791191516498 t + 5) / ((t - 1) / 2 (t - 223602414174936635551215229139542233209282 t + 1)) infinity ----- \ i 2 ) c(i) t = (7721633254470290932660510486672502551445 t / ----- i = 0 / - 312614168384135721247328110968401448370918 t + 17) / ((t - 1) / 2 (t - 223602414174936635551215229139542233209282 t + 1)) In Maple notation, these generating functions are 18*(1115023214533194150193179162539677253619*t^2+ 20902567364856755819122982741206134454174*t-1)/(t-1)/(t^2-\ 223602414174936635551215229139542233209282*t+1) -(19190443461097430763218924729937754302953*t^2+ 285702091668567999551448675751791191516498*t+5)/(t-1)/(t^2-\ 223602414174936635551215229139542233209282*t+1) (7721633254470290932660510486672502551445*t^2-\ 312614168384135721247328110968401448370918*t+17)/(t-1)/(t^2-\ 223602414174936635551215229139542233209282*t+1) Then for all i>=0 we have 3 3 3 76 a(i) + 93 b(i) + 93 c(i) = -2052 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 626, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 23 (2531092290531198159578643758329187357237145479 t / ----- i = 0 / + 10315568206794438725729413395082637099182094522 t - 1) / ((t - 1) / 2 (t - 58991939423186361945252833397386161839138302402 t + 1)) infinity ----- \ i 2 ) b(i) t = - (88088270005414828629008244755853957987344431867 t / ----- i = 0 / - 34428113298120691185698326664803437933464095894 t + 27) / ((t - 1) / 2 (t - 58991939423186361945252833397386161839138302402 t + 1)) infinity ----- \ i 2 ) c(i) t = (81031891498479367093213237914451375052016632351 t / ----- i = 0 / - 134692048205773504536523156005501895105896968382 t + 31) / ((t - 1) / 2 (t - 58991939423186361945252833397386161839138302402 t + 1)) In Maple notation, these generating functions are 23*(2531092290531198159578643758329187357237145479*t^2+ 10315568206794438725729413395082637099182094522*t-1)/(t-1)/(t^2-\ 58991939423186361945252833397386161839138302402*t+1) -(88088270005414828629008244755853957987344431867*t^2-\ 34428113298120691185698326664803437933464095894*t+27)/(t-1)/(t^2-\ 58991939423186361945252833397386161839138302402*t+1) (81031891498479367093213237914451375052016632351*t^2-\ 134692048205773504536523156005501895105896968382*t+31)/(t-1)/(t^2-\ 58991939423186361945252833397386161839138302402*t+1) Then for all i>=0 we have 3 3 3 76 a(i) + 99 b(i) + 99 c(i) = -76000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 627, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 26 (1425657563915356380765514290422745023999 t / ----- i = 0 / + 5308908659765506683322239206598821856002 t - 1) / ((t - 1) / 2 (t - 22029185486252786506338329204543074080002 t + 1)) infinity ----- \ i 2 ) b(i) t = - 5 (7577090134616102074757316891712600605361 t / ----- i = 0 / + 19015812389662177716768684096526407074638 t + 1) / ((t - 1) / 2 (t - 22029185486252786506338329204543074080002 t + 1)) infinity ----- \ i 2 ) c(i) t = 27 (648094352188552375142212226130287006801 t / ----- i = 0 / - 5572705930758604188387767964693066206802 t + 1) / ((t - 1) / 2 (t - 22029185486252786506338329204543074080002 t + 1)) In Maple notation, these generating functions are 26*(1425657563915356380765514290422745023999*t^2+ 5308908659765506683322239206598821856002*t-1)/(t-1)/(t^2-\ 22029185486252786506338329204543074080002*t+1) -5*(7577090134616102074757316891712600605361*t^2+ 19015812389662177716768684096526407074638*t+1)/(t-1)/(t^2-\ 22029185486252786506338329204543074080002*t+1) 27*(648094352188552375142212226130287006801*t^2-\ 5572705930758604188387767964693066206802*t+1)/(t-1)/(t^2-\ 22029185486252786506338329204543074080002*t+1) Then for all i>=0 we have 3 3 3 77 a(i) + 80 b(i) + 80 c(i) = -211288 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 628, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 8 (4622053089682290779 t + 6677495371105690994 t - 1) ) a(i) t = ------------------------------------------------------ / 2 ----- (t - 1) (t - 24374262199437733634 t + 1) i = 0 infinity ----- 2 \ i 3 (12560533209661457861 t + 4840548329163074778 t + 1) ) b(i) t = - ------------------------------------------------------- / 2 ----- (t - 1) (t - 24374262199437733634 t + 1) i = 0 infinity ----- 2 \ i 3 (7630343247333681031 t - 25031424786158213674 t + 3) ) c(i) t = ------------------------------------------------------- / 2 ----- (t - 1) (t - 24374262199437733634 t + 1) i = 0 In Maple notation, these generating functions are 8*(4622053089682290779*t^2+6677495371105690994*t-1)/(t-1)/(t^2-\ 24374262199437733634*t+1) -3*(12560533209661457861*t^2+4840548329163074778*t+1)/(t-1)/(t^2-\ 24374262199437733634*t+1) 3*(7630343247333681031*t^2-25031424786158213674*t+3)/(t-1)/(t^2-\ 24374262199437733634*t+1) Then for all i>=0 we have 3 3 3 78 a(i) + 95 b(i) + 95 c(i) = -26754 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 629, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 2 (510193190323799518347983289298333813882373555738785527\ / ----- i = 0 2 1516965116834525475644136287423 t + 34971248184188326504119683274866126\ / 5065847755016593023748121376896004127653237935361006 t - 13) / ((t - 1) ( / 2 t - 1400407251916554959747807404031056699898345875877221689684604024842\ 989949579853368467522 t + 1)) infinity ----- \ i ) b(i) t = - (127235352029480529659267901238638899269490782099511293\ / ----- i = 0 2 90666766747969343381816029688633 t + 2607996602757108796522236755650328\ / 01631455032885905984203169621438709745337875129243758 t + 25) / ((t - 1) / 2 (t - 140040725191655495974780740403105669989834587587722168968460402484\ 2989949579853368467522 t + 1)) infinity ----- \ i ) c(i) t = 8 (125976112886234026625604478167851062075968895307986351\ / ----- i = 0 2 7346135141479115345601920803561 t - 35450160563694706843524852992790597\ / 2 065560202840062002716575683664814001435563315670117 t + 4) / ((t - 1) (t / - 140040725191655495974780740403105669989834587587722168968460402484298\ 9949579853368467522 t + 1)) In Maple notation, these generating functions are 2*(5101931903237995183479832892983338138823735557387855271516965116834525475644\ 136287423*t^2+34971248184188326504119683274866126506584775501659302374812137689\ 6004127653237935361006*t-13)/(t-1)/(t^2-140040725191655495974780740403105669989\ 8345875877221689684604024842989949579853368467522*t+1) -(12723535202948052965926790123863889926949078209951129390666766747969343381816\ 029688633*t^2+26079966027571087965222367556503280163145503288590598420316962143\ 8709745337875129243758*t+25)/(t-1)/(t^2-140040725191655495974780740403105669989\ 8345875877221689684604024842989949579853368467522*t+1) 8*(1259761128862340266256044781678510620759688953079863517346135141479115345601\ 920803561*t^2-35450160563694706843524852992790597065560202840062002716575683664\ 814001435563315670117*t+4)/(t-1)/(t^2-14004072519165549597478074040310566998983\ 45875877221689684604024842989949579853368467522*t+1) Then for all i>=0 we have 3 3 3 79 a(i) + 81 b(i) + 81 c(i) = -79 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 630, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 24 (10329878686978896878066997598936581797234085280598074\ / ----- i = 0 2 78819115878336453156463 t + 1777603826109608649993773134421187792548054\ / 2 397566234337033370797617257571186 t - 1) / ((t - 1) (t - 747751263039\ / 4912609826999676870311560998035316874923733964349385324703357954 t + 1)) infinity ----- \ i ) b(i) t = - (384821905721193087495499235782974374134837766302009368\ / ----- i = 0 2 49108294921740257422373 t - 2405008857051299538640011331778158659687808\ / 2 0493145677506835582838973563286210 t + 29) / ((t - 1) (t - 7477512630\ / 394912609826999676870311560998035316874923733964349385324703357954 t + 1)) infinity ----- \ i ) c(i) t = 7 (499150255420583283141813613899253603226580881097900364\ / ----- i = 0 2 1879577211675651555133 t - 70532314115781633118681090333519432917809082\ / 2 59129754976489964652070893574594 t + 5) / ((t - 1) (t - 7477512630394\ / 912609826999676870311560998035316874923733964349385324703357954 t + 1)) In Maple notation, these generating functions are 24*( 1032987868697889687806699759893658179723408528059807478819115878336453156463*t^ 2+1777603826109608649993773134421187792548054397566234337033370797617257571186* t-1)/(t-1)/(t^2-\ 7477512630394912609826999676870311560998035316874923733964349385324703357954*t+ 1) -(38482190572119308749549923578297437413483776630200936849108294921740257422373 *t^2-\ 24050088570512995386400113317781586596878080493145677506835582838973563286210*t +29)/(t-1)/(t^2-\ 7477512630394912609826999676870311560998035316874923733964349385324703357954*t+ 1) 7*(4991502554205832831418136138992536032265808810979003641879577211675651555133 *t^2-\ 7053231411578163311868109033351943291780908259129754976489964652070893574594*t+ 5)/(t-1)/(t^2-\ 7477512630394912609826999676870311560998035316874923733964349385324703357954*t+ 1) Then for all i>=0 we have 3 3 3 79 a(i) + 84 b(i) + 84 c(i) = -460728 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 631, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 4 (3443562796482490251988143871758213113 t / ----- i = 0 / + 24845353509330306829471919823242465294 t - 7) / ((t - 1) / 2 (t - 28169888607471368762744242950140928002 t + 1)) infinity ----- \ i 2 ) b(i) t = - (18806414838365830640527047748754662109 t / ----- i = 0 / + 9403149668552680895122468783006182662 t + 29) / ((t - 1) / 2 (t - 28169888607471368762744242950140928002 t + 1)) infinity ----- \ i 2 ) c(i) t = 5 (3302141261475500761173657033516504007 t / ----- i = 0 / - 8944054162859203068303560339868672974 t + 7) / ((t - 1) / 2 (t - 28169888607471368762744242950140928002 t + 1)) In Maple notation, these generating functions are 4*(3443562796482490251988143871758213113*t^2+ 24845353509330306829471919823242465294*t-7)/(t-1)/(t^2-\ 28169888607471368762744242950140928002*t+1) -(18806414838365830640527047748754662109*t^2+ 9403149668552680895122468783006182662*t+29)/(t-1)/(t^2-\ 28169888607471368762744242950140928002*t+1) 5*(3302141261475500761173657033516504007*t^2-\ 8944054162859203068303560339868672974*t+7)/(t-1)/(t^2-\ 28169888607471368762744242950140928002*t+1) Then for all i>=0 we have 3 3 3 79 a(i) + 96 b(i) + 96 c(i) = -40448 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 632, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 15 (57305290010280177444230825908200178833852177599 t / ----- i = 0 / + 344516398200548617113796318530251470658675342402 t - 1) / ((t - 1) / 2 (t - 2375516937001973754901803247555640715155001120002 t + 1)) infinity ----- \ i 2 ) b(i) t = - 11 (89769760076049294985357718253595881335710362001 t / ----- i = 0 / + 113695126380454121979181184068619781370686437998 t + 1) / ((t - 1) / 2 (t - 2375516937001973754901803247555640715155001120002 t + 1)) infinity ----- \ i 2 ) c(i) t = 16 (48285782706124473713941831477112751504116769751 t / ----- i = 0 / - 188167892144970572877062326823636019614764569752 t + 1) / ((t - 1) / 2 (t - 2375516937001973754901803247555640715155001120002 t + 1)) In Maple notation, these generating functions are 15*(57305290010280177444230825908200178833852177599*t^2+ 344516398200548617113796318530251470658675342402*t-1)/(t-1)/(t^2-\ 2375516937001973754901803247555640715155001120002*t+1) -11*(89769760076049294985357718253595881335710362001*t^2+ 113695126380454121979181184068619781370686437998*t+1)/(t-1)/(t^2-\ 2375516937001973754901803247555640715155001120002*t+1) 16*(48285782706124473713941831477112751504116769751*t^2-\ 188167892144970572877062326823636019614764569752*t+1)/(t-1)/(t^2-\ 2375516937001973754901803247555640715155001120002*t+1) Then for all i>=0 we have 3 3 3 79 a(i) + 100 b(i) + 100 c(i) = -9875 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 633, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 26 (21043516510906442856519479 t + 2592093713040213775648953722 t - 1) ----------------------------------------------------------------------- 2 (t - 1) (t - 101100763256626275757604246402 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 2 (274061670403617759352383983 t + 31030073741625160284859940014 t + 3) - ------------------------------------------------------------------------ 2 (t - 1) (t - 101100763256626275757604246402 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 26 (5493876946045596466721661 t - 2413504293255951599867669662 t + 1) ---------------------------------------------------------------------- 2 (t - 1) (t - 101100763256626275757604246402 t + 1) In Maple notation, these generating functions are 26*(21043516510906442856519479*t^2+2592093713040213775648953722*t-1)/(t-1)/(t^2 -101100763256626275757604246402*t+1) -2*(274061670403617759352383983*t^2+31030073741625160284859940014*t+3)/(t-1)/(t ^2-101100763256626275757604246402*t+1) 26*(5493876946045596466721661*t^2-2413504293255951599867669662*t+1)/(t-1)/(t^2-\ 101100763256626275757604246402*t+1) Then for all i>=0 we have 3 3 3 80 a(i) + 81 b(i) + 81 c(i) = -80 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 634, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 6634705897896884674157039737 t + 39341722856987500164939912286 t - 23 ---------------------------------------------------------------------- 2 (t - 1) (t - 7525439670291003426447830402 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 2 (3139312737688004460671594681 t + 15228994149856604494415565318 t + 1) - ------------------------------------------------------------------------- 2 (t - 1) (t - 7525439670291003426447830402 t + 1) infinity ----- \ i ) c(i) t = 2 / ----- i = 0 2 (1128795798931372741230067491 t - 19497102686475981696317227502 t + 11) / 2 / ((t - 1) (t - 7525439670291003426447830402 t + 1)) / In Maple notation, these generating functions are (6634705897896884674157039737*t^2+39341722856987500164939912286*t-23)/(t-1)/(t^ 2-7525439670291003426447830402*t+1) -2*(3139312737688004460671594681*t^2+15228994149856604494415565318*t+1)/(t-1)/( t^2-7525439670291003426447830402*t+1) 2*(1128795798931372741230067491*t^2-19497102686475981696317227502*t+11)/(t-1)/( t^2-7525439670291003426447830402*t+1) Then for all i>=0 we have 3 3 3 80 a(i) + 99 b(i) + 99 c(i) = -80000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 635, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 4 (1535682661693 t + 3601621218199 t - 2) ) a(i) t = ------------------------------------------ / 2 ----- (t - 1) (t - 8195978831042 t + 1) i = 0 infinity ----- 2 \ i 9 (1028691789451 t - 502801963172 t + 1) ) b(i) t = - ----------------------------------------- / 2 ----- (t - 1) (t - 8195978831042 t + 1) i = 0 infinity ----- 2 \ i 8313190620941 t - 13046199057472 t + 11 ) c(i) t = ---------------------------------------- / 2 ----- (t - 1) (t - 8195978831042 t + 1) i = 0 In Maple notation, these generating functions are 4*(1535682661693*t^2+3601621218199*t-2)/(t-1)/(t^2-8195978831042*t+1) -9*(1028691789451*t^2-502801963172*t+1)/(t-1)/(t^2-8195978831042*t+1) (8313190620941*t^2-13046199057472*t+11)/(t-1)/(t^2-8195978831042*t+1) Then for all i>=0 we have 3 3 3 86 a(i) + 91 b(i) + 91 c(i) = -10750 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 636, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = (36923435220999172832259223583223671293467756600107175913 t / ----- i = 0 / + 168337905564698449415991824655957954483552094515245681710 t - 23) / ( / (t - 1) 2 (t - 38459891113034181052369444644606894128407303432058628098 t + 1)) infinity ----- \ i ) b(i) t = - 9 ( / ----- i = 0 2 4222207804700086892699004259942221906611574993632174049 t / + 9680222375139226337616209419508128158801388636171105310 t + 1) / ( / (t - 1) 2 (t - 38459891113034181052369444644606894128407303432058628098 t + 1)) infinity ----- \ i 2 ) c(i) t = (22335382572785981438787125304172985095608763051735006967 t / ----- i = 0 / - 147457254191339800511624048419226135684325435719964521230 t + 23) / ( / (t - 1) 2 (t - 38459891113034181052369444644606894128407303432058628098 t + 1)) In Maple notation, these generating functions are (36923435220999172832259223583223671293467756600107175913*t^2+ 168337905564698449415991824655957954483552094515245681710*t-23)/(t-1)/(t^2-\ 38459891113034181052369444644606894128407303432058628098*t+1) -9*(4222207804700086892699004259942221906611574993632174049*t^2+ 9680222375139226337616209419508128158801388636171105310*t+1)/(t-1)/(t^2-\ 38459891113034181052369444644606894128407303432058628098*t+1) (22335382572785981438787125304172985095608763051735006967*t^2-\ 147457254191339800511624048419226135684325435719964521230*t+23)/(t-1)/(t^2-\ 38459891113034181052369444644606894128407303432058628098*t+1) Then for all i>=0 we have 3 3 3 86 a(i) + 99 b(i) + 99 c(i) = -86000 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 637, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 9 (1484467512817993325437 t + 2307287447594424594566 t - 3) ) a(i) t = ------------------------------------------------------------ / 2 ----- (t - 1) (t - 2346044459057229542402 t + 1) i = 0 infinity ----- \ i ) b(i) t = / ----- i = 0 2 2 (6689758297589896583521 t + 6691526238969117816478 t + 1) - ------------------------------------------------------------ 2 (t - 1) (t - 2346044459057229542402 t + 1) infinity ----- 2 \ i 32 (177240765918564331021 t - 1013571049453502731022 t + 1) ) c(i) t = ------------------------------------------------------------ / 2 ----- (t - 1) (t - 2346044459057229542402 t + 1) i = 0 In Maple notation, these generating functions are 9*(1484467512817993325437*t^2+2307287447594424594566*t-3)/(t-1)/(t^2-\ 2346044459057229542402*t+1) -2*(6689758297589896583521*t^2+6691526238969117816478*t+1)/(t-1)/(t^2-\ 2346044459057229542402*t+1) 32*(177240765918564331021*t^2-1013571049453502731022*t+1)/(t-1)/(t^2-\ 2346044459057229542402*t+1) Then for all i>=0 we have 3 3 3 90 a(i) + 97 b(i) + 97 c(i) = -1406250 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 638, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = 8 ( / ----- i = 0 2 51174049607385584691545849006786889078110497679362156274 t / + 67070393510513388052350297137124685031451785169294867527 t - 1) / ( / (t - 1) 2 (t - 268587133903296269014744308697210644277005932038559092802 t + 1)) infinity ----- \ i ) b(i) t = - 8 ( / ----- i = 0 2 69709473930438902353469134256573784320489021171879690776 t / - 34383655402110581540289392631176695535294773833640067777 t + 1) / ( / (t - 1) 2 (t - 268587133903296269014744308697210644277005932038559092802 t + 1)) infinity ----- \ i ) c(i) t = ( / ----- i = 0 2 475797312071694283321279715641731252038935373088058076171 t / - 758403860298320849826717648644907962320489351793975060182 t + 11) / ( / (t - 1) 2 (t - 268587133903296269014744308697210644277005932038559092802 t + 1)) In Maple notation, these generating functions are 8*(51174049607385584691545849006786889078110497679362156274*t^2+ 67070393510513388052350297137124685031451785169294867527*t-1)/(t-1)/(t^2-\ 268587133903296269014744308697210644277005932038559092802*t+1) -8*(69709473930438902353469134256573784320489021171879690776*t^2-\ 34383655402110581540289392631176695535294773833640067777*t+1)/(t-1)/(t^2-\ 268587133903296269014744308697210644277005932038559092802*t+1) (475797312071694283321279715641731252038935373088058076171*t^2-\ 758403860298320849826717648644907962320489351793975060182*t+11)/(t-1)/(t^2-\ 268587133903296269014744308697210644277005932038559092802*t+1) Then for all i>=0 we have 3 3 3 91 a(i) + 95 b(i) + 95 c(i) = -31213 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 639, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- 2 \ i 4 (60525783360893 t + 837213868103114 t - 7) ) a(i) t = --------------------------------------------- / 2 ----- (t - 1) (t - 1367039850144002 t + 1) i = 0 infinity ----- 2 \ i 16 (16213709059326 t + 112138613038673 t + 1) ) b(i) t = - ---------------------------------------------- / 2 ----- (t - 1) (t - 1367039850144002 t + 1) i = 0 infinity ----- 2 \ i 164045383289629 t - 2217682536857658 t + 29 ) c(i) t = -------------------------------------------- / 2 ----- (t - 1) (t - 1367039850144002 t + 1) i = 0 In Maple notation, these generating functions are 4*(60525783360893*t^2+837213868103114*t-7)/(t-1)/(t^2-1367039850144002*t+1) -16*(16213709059326*t^2+112138613038673*t+1)/(t-1)/(t^2-1367039850144002*t+1) (164045383289629*t^2-2217682536857658*t+29)/(t-1)/(t^2-1367039850144002*t+1) Then for all i>=0 we have 3 3 3 91 a(i) + 99 b(i) + 99 c(i) = -11375 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 640, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i 2 ) a(i) t = 7 (7324661403962448106773719247174698883276262665853519 t / ----- i = 0 / + 7852018878695114537965817404920744896576445529133682 t - 1) / ((t - 1) / 2 (t - 29308134650531546594937782901154011266327130701614402 t + 1)) infinity ----- \ i ) b(i) t = - 4 ( / ----- i = 0 2 14409625364626851575232051444920241670872428218817641 t / - 508120698005254937832889084529786968941228563629642 t + 1) / ((t - 1) / 2 (t - 29308134650531546594937782901154011266327130701614402 t + 1)) infinity ----- \ i 2 ) c(i) t = (39326847948601286033993907661744219475299056210636769 t / ----- i = 0 / - 94932866615087672583590557103306038283023854831388778 t + 9) / ( / 2 (t - 1) (t - 29308134650531546594937782901154011266327130701614402 t + 1)) In Maple notation, these generating functions are 7*(7324661403962448106773719247174698883276262665853519*t^2+ 7852018878695114537965817404920744896576445529133682*t-1)/(t-1)/(t^2-\ 29308134650531546594937782901154011266327130701614402*t+1) -4*(14409625364626851575232051444920241670872428218817641*t^2-\ 508120698005254937832889084529786968941228563629642*t+1)/(t-1)/(t^2-\ 29308134650531546594937782901154011266327130701614402*t+1) (39326847948601286033993907661744219475299056210636769*t^2-\ 94932866615087672583590557103306038283023854831388778*t+9)/(t-1)/(t^2-\ 29308134650531546594937782901154011266327130701614402*t+1) Then for all i>=0 we have 3 3 3 95 a(i) + 98 b(i) + 98 c(i) = -32585 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ------------------------------------------ Theorem Number , 641, : Let a(i), b(i), c(i) be defined in terms of the follo\ wing generating functions infinity ----- \ i ) a(i) t = / ----- i = 0 2 17 (63916368080238662357282759 t + 80448700098021148080928442 t - 1) --------------------------------------------------------------------- 2 (t - 1) (t - 289687464394836993624686402 t + 1) infinity ----- \ i ) b(i) t = / ----- i = 0 2 7 (168496247432668003541343001 t + 46328164365750441169098598 t + 1) - --------------------------------------------------------------------- 2 (t - 1) (t - 289687464394836993624686402 t + 1) infinity ----- \ i ) c(i) t = / ----- i = 0 2 21 (34214339904544743401178841 t - 105822477170684224971326042 t + 1) ---------------------------------------------------------------------- 2 (t - 1) (t - 289687464394836993624686402 t + 1) In Maple notation, these generating functions are 17*(63916368080238662357282759*t^2+80448700098021148080928442*t-1)/(t-1)/(t^2-\ 289687464394836993624686402*t+1) -7*(168496247432668003541343001*t^2+46328164365750441169098598*t+1)/(t-1)/(t^2-\ 289687464394836993624686402*t+1) 21*(34214339904544743401178841*t^2-105822477170684224971326042*t+1)/(t-1)/(t^2-\ 289687464394836993624686402*t+1) Then for all i>=0 we have 3 3 3 98 a(i) + 99 b(i) + 99 c(i) = -401408 Proof: Since everything is in the C-finite ansatz, checking it for i from 0 \ to 10 suffices, which we did and you are welcome to check. ----------------------------------------------------- This ends this fascinating article that stated, 641, theorems and took, 6812.723, seconds to generate