> #ok to post
;
> #Yifan Zhang, 11/5/2020, hw17
;
> 
;
> #Q1.
;
> #Use the appropriate procedure in ComboProject1.txt to find the number of ways a King can travel on a 3 by 50 chessboard, return to the starting square and visit each of the 150 squares exaxtly once.
;
> read `ComboProject1.txt`
``
`This is ComboProject1.txt, a Maple package that is part of Project 1 in Dr. Z.\
's Combinatorics Class at Rutgers University, Fall 2020`
`Its purpose is to generate and investigate integer sequences counting  `
`the number of HAMILTONIAN CYCLES for interesting graphs that come from Chess. \
Generalizing and Extending Euler's Knight's tour`
``
`-----------------------------------------`
`-----------------`
``
`Team Leader: tbd `
``
`Other Team members: tbd `
``
`-----------------`
``
`------------------------------------`
`Added Oct. 27, 2020: William Wang detected a bug in SAW and SAWnu, that is now\
 fixed. He won 5 dollars.`
`------------------------------------`
`For a list of all the functions type: Help(); `
`For Help with any of the functions, type  Help(FunctionName):`

;
> 
;
> KiTours(3,3)[1]
[[1, 1], [1, 2], [1, 3], [2, 2], [2, 3], [3, 3], [3, 2], [3, 1], [2, 1], [1, 1]
]

;
> nops(KiTours(3,3))
32

;
> #There are 32 ways of return to the starting square and visit each of the squares exactly once in a 3 by 3 board. 
;
> #running the code: nops(KiTours(3,10)) will get the number of ways of a 3 by 10 board. 
;
> #nops(KiTours(3,10))
;
> #My laptop is stucked by running this board since its too large. 
;
> 
;
> #Q2.
;
> #Use the appropriate procedures in ComboProject2.txt to find the number of ways of walking from [0,0] to [3000,3000] using, as #atomic steps {[1,0],[0,1],[1,1],[1,2],[2,1]}, all the while staying in the region x ≥ y
> #Don't do it directly! Use Findrec followed by SeqFromRec.
;
> read `ComboProject2.txt`
`----------------------`
``
`Team Leader: tbd `
``
`Other Team members: tbd `
`----------------------`
`This is ComboProject2.txt, a Maple package that is part of Project 2 in Dr. Z.\
's Combinatorics Class at Rutgers University`
`Its purpose is to create a database of sequences enumerating`
`Lattice Walks to the diagonal in the 2-Dimensional Manhattan Lattice for many \
sets of atomic steps`
`and also counting those walks that stay in x>=y `
`It also finds their recurrences, growth rates, critical exponents, asymptotics\
, and congruence properties`
`The final output is a list of lists arranged in LEXICGORAPHIC ORDER`
`For a list of all the functions type: Help(); `
`For Help with any of the functions, type  Help(FunctionName):`

;
> #
;
> #
;
> #NuGW([3000,3000], {[1,0],[0,1],[1,1],[1,2],[2,1]})
;
> A:=InfoGA({[1,0],[0,1],[1,1],[1,2],[2,1]},  n, N, 100, 10, 2)[2]
Typesetting:-mprintslash([(A := [2, 8, 37, 187, 1005, 5633, 32566, 192792, 
1162918, 7121902, 44165560, 276783968, 1750207940, 11153013440, 71550898197, 
461746445731, 2995462031745, 19523143468973, 127777132138891, 839452832023207,
5533837097342891, 36594085887854795, 242680221398481381, 1613598426851118817, 
10754859380597438069, 71842748551816723277, 480905190308830819225, 
3225307676284611819217, 21670117616522081549953, 145840679672699944094433, 
983053428271497814915238, 6636125814739273692660888, 44859345005089675067344174
, 303638741080314921979131686, 2057763386337603966845020668, 
13961702500509954172092227612, 94832904877320251327289447656, 
644811242965640714216092401476, 4388701626430898296019153105026, 
29898414203468535846138390257098, 203868052178975450132547578090878, 
1391299997423028635726671660812258, 9502676021281003270491972199172678, 
64954415289919470625783673910590162, 444318286253185235104169038220769834, 
3041505111745155334565491437675951478, 20834291953518436333856265143938254112,
142808006475300877885644385533683789544, 
979486623322036695091659490280293252388, 
6722113044436452619618838139392108932544, 
46159840685590887130990146271863301948932, 
317149767247329603835205219424547271877640, 
2180203616630012152899981082853344330863600, 
14995250755906462987896738691799833800057188, 
103187322871762288166267391213852436341593440, 
710407013750971034635819594510254277572365908, 
4893157170571776194472453475384072493044630796, 
33718266588298580690524800941934001781023110080, 
232449667852724654835837303938633160969451478544, 
1603149509313335574652782178094291978073641328844, 
11061005888953858476706566126351543539052272903756, 
76345791014820550417385680327774598631812365390368, 
527157144730437642987584509108354471713065062625621, 
3641283643303109158841814353820675448155573305734211, 
25160743257556118964998005719667382275056372270781361, 
173917110784122314616054203855263522307332578924194557, 
1202559579297119194159083942232889267537494006925283523, 
8317869180316846721598239799022640050445573573445684655, 
57551241343288109817138391092180764447681302048248820131, 
398318554948514061845085225547846089467734966995353286467, 
2757629281094817943980892956461722313717173544306844753417, 
19097088120874508128459436210573544074663528849756841343837, 
132288142556896045959875193265324081279508027592435887834873, 
916629626171229062090452158227727464778545824380718054761425, 
6353059242748725566023984612140876384585725672934570546756325, 
44043814816772341087901705777902157474143331399221938369818749, 
305419695107616899368578836562967396449265469116289492687533533, 
2118441286214424795488375375242088592503725825701269256579767213, 
14697396286823356190808581001042069544758294571601291462019462715, 
101992058240747051261997364270795867830034119767083551452240782119, 
707932389395598767489001310274946005312379288732982749246937512211, 
4914895296468833780765306183111901447633106633991384356972954580803, 
34129623106926486002513939838826278425011873880804610789295353402559, 
237050679570211885103583062835146196552717477089982972091632360381263, 
1646801454510925919757511591374329782023186918978408163854645091260623, 
11442726400624088077490918201249088270923656651263586288494119028220439, 
79525059431914254320173991674495198118683400923035173498797993217200155, 
552793282860951143053805456010581331408772694121789555555805068282359851, 
3843296530698343279345179930567104750355511651302919535147197816686234091, 
26725484701388444806278417713424707745964810248783699190670212084087619139, 
185877184107020524483042497713140285413211254689628201596275812342514092131, 
1293015322548665854131920399078826854475549179564799023521177926734074015163, 
8996150254760647906323215165109779404945373838351436806306969229807469579427, 
62601331989171111451520743222389803118190473819347767731975787964854524533995,
435695168699446738002543509264876646476963654139011730412756863836545742727205,
3032862433475797288961125692701615427437646073674378686183898904457046900416001
, 21115045581629220700932659100213290244316033366973480005557635331787446395635\
397, 14702773598692204628841829117868195528751840926724044777440016372044409106\
6093117, 1023936642098208262411944997238078841046747930943878748613313510857794\
189695533841, 71320132678949415607790606846678597710303874983603001025584198812\
47499606292436761])],[[2, 8, 37, 187, 1005, 5633, 32566, 192792, 1162918, 
7121902, 44165560, 276783968, 1750207940, 11153013440, 71550898197, 
461746445731, 2995462031745, 19523143468973, 127777132138891, 839452832023207,
5533837097342891, 36594085887854795, 242680221398481381, 1613598426851118817, 
10754859380597438069, 71842748551816723277, 480905190308830819225, 
3225307676284611819217, 21670117616522081549953, 145840679672699944094433, 
983053428271497814915238, 6636125814739273692660888, 44859345005089675067344174
, 303638741080314921979131686, 2057763386337603966845020668, 
13961702500509954172092227612, 94832904877320251327289447656, 
644811242965640714216092401476, 4388701626430898296019153105026, 
29898414203468535846138390257098, 203868052178975450132547578090878, 
1391299997423028635726671660812258, 9502676021281003270491972199172678, 
64954415289919470625783673910590162, 444318286253185235104169038220769834, 
3041505111745155334565491437675951478, 20834291953518436333856265143938254112,
142808006475300877885644385533683789544, 
979486623322036695091659490280293252388, 
6722113044436452619618838139392108932544, 
46159840685590887130990146271863301948932, 
317149767247329603835205219424547271877640, 
2180203616630012152899981082853344330863600, 
14995250755906462987896738691799833800057188, 
103187322871762288166267391213852436341593440, 
710407013750971034635819594510254277572365908, 
4893157170571776194472453475384072493044630796, 
33718266588298580690524800941934001781023110080, 
232449667852724654835837303938633160969451478544, 
1603149509313335574652782178094291978073641328844, 
11061005888953858476706566126351543539052272903756, 
76345791014820550417385680327774598631812365390368, 
527157144730437642987584509108354471713065062625621, 
3641283643303109158841814353820675448155573305734211, 
25160743257556118964998005719667382275056372270781361, 
173917110784122314616054203855263522307332578924194557, 
1202559579297119194159083942232889267537494006925283523, 
8317869180316846721598239799022640050445573573445684655, 
57551241343288109817138391092180764447681302048248820131, 
398318554948514061845085225547846089467734966995353286467, 
2757629281094817943980892956461722313717173544306844753417, 
19097088120874508128459436210573544074663528849756841343837, 
132288142556896045959875193265324081279508027592435887834873, 
916629626171229062090452158227727464778545824380718054761425, 
6353059242748725566023984612140876384585725672934570546756325, 
44043814816772341087901705777902157474143331399221938369818749, 
305419695107616899368578836562967396449265469116289492687533533, 
2118441286214424795488375375242088592503725825701269256579767213, 
14697396286823356190808581001042069544758294571601291462019462715, 
101992058240747051261997364270795867830034119767083551452240782119, 
707932389395598767489001310274946005312379288732982749246937512211, 
4914895296468833780765306183111901447633106633991384356972954580803, 
34129623106926486002513939838826278425011873880804610789295353402559, 
237050679570211885103583062835146196552717477089982972091632360381263, 
1646801454510925919757511591374329782023186918978408163854645091260623, 
11442726400624088077490918201249088270923656651263586288494119028220439, 
79525059431914254320173991674495198118683400923035173498797993217200155, 
552793282860951143053805456010581331408772694121789555555805068282359851, 
3843296530698343279345179930567104750355511651302919535147197816686234091, 
26725484701388444806278417713424707745964810248783699190670212084087619139, 
185877184107020524483042497713140285413211254689628201596275812342514092131, 
1293015322548665854131920399078826854475549179564799023521177926734074015163, 
8996150254760647906323215165109779404945373838351436806306969229807469579427, 
62601331989171111451520743222389803118190473819347767731975787964854524533995,
435695168699446738002543509264876646476963654139011730412756863836545742727205,
3032862433475797288961125692701615427437646073674378686183898904457046900416001
, 21115045581629220700932659100213290244316033366973480005557635331787446395635\
397, 14702773598692204628841829117868195528751840926724044777440016372044409106\
6093117, 1023936642098208262411944997238078841046747930943878748613313510857794\
189695533841, 71320132678949415607790606846678597710303874983603001025584198812\
47499606292436761]])

;
> ope:=Findrec(A, n, N, 10)
Typesetting:-mprintslash([(ope := -2*(2*n+3)/(n+5)-(11*n+23)/(n+5)*N-(13*n+41)/
(n+5)*N^2-5*(n+3)/(n+5)*N^3+N^4)],[-2*(2*n+3)/(n+5)-(11*n+23)/(n+5)*N-(13*n+41)
/(n+5)*N^2-5*(n+3)/(n+5)*N^3+N^4])

;
> SeqFromRec(ope, n, N, [2,8,37, 187], 3000)[3000]
9516909136130449766101673419767813477034982293030856927691691446756534787154068\
329180875228282470757065198587282037236315256313155149

;
> #The answer is 9516909136130449766101673419767813477034982293030856927691691446756534787154068\
> 329180875228282470757065198587282037236315256313155149. If I directly use NuGW(), my computer will run out of memory. 
;
> 
;
> #Q3.
;
> #Use the appropriate procedures in ComboProject3.txt to find the number of ways of walking from [0,0,0] to [3000,3000,3000] #using, as atomic steps {[1,0,0],[0,1,0],[0,0,1],[1,1,1]}, all the while staying in the region x ≥ y ≥ z
> #Don't do it directly! Use Findrec followed by SeqFromRec.
;
> read `ComboProject3.txt` 
`---------------------`
``
`Team Leader: tbd `
``
`Other Team members: tbd `
`---------------------`
`This is ComboProject3.txt, a Maple package that is part of Project 3 in Dr. Z.\
's Combinatorics Class at Rutgers University, Fall 2020`
`Its purpose is to create a database of sequences enumerating`
`Lattice Walks to the diagonal in the 3-Dimensional Manhattan Lattice for many \
sets of atomic steps`
`and also counting those walks that stay in x>=y>=z `
`It also finds their recurrences, growth rates, critical exponents, asymptotics\
, and congruence properties`
`The final output is a list of lists arranged in LEXICGORAPHIC ORDER`
`For a list of all the functions type: Help(); `
`For Help with any of the functions, type  Help(FunctionName):`

;
> A:=InfoGA({[1,0,0],[0,1,0],[0,0,1],[1,1,1]}, n, N, 50, 10, 2)[2]
Typesetting:-mprintslash([(A := [2, 10, 88, 1043, 14778, 236001, 4107925, 
76314975, 1491934038, 30389576308, 640286048416, 13877540824735, 
308102204007536, 6983346070924707, 161156356282624227, 3778249609096250059, 
89826197363219012470, 2162338803354415120414, 52637415804379149938876, 
1294313658632145337351381, 32118082448138745067175242, 
803656789698224684452667975, 20262539635339176715000960941, 
514456553505357928725536149803, 13146084523635788235064716197728, 
337929024350121818044901686404816, 8734691492940974137071498064995420, 
226931194428057541769204674879130191, 5923987397778903817189358328568041496, 
155335609958542073698381974113868127891, 
4090172312867860136825480052716884724147, 
108121976818168155620957000319917917053675, 
2868707794254575240567639311917494731749030, 
76377538885644568975349924729052848698617526, 
2040172740682907191699950846063214773112927416, 
54665344392211673342456683384055104205997175257, 
1469025374919143636369316715736858925903810273670, 
39586979783512218527277338099905807341274587256147, 
1069596920795621360143277142155882112468901055822299, 
28971834889893726116466068771262180074158013962368089, 
786624416885179957698948378595042627165085805977597238, 
21406496941578870323675397740377275998112856431253739940, 
583801369714608515305502011392156725334624008192909440168, 
15954513928133137501267139726262869284981213941344807489857, 
436879272160793629128022091511848928647620180950721848780592, 
11985652641165379506890719555297678340424492500261026978221269, 
329419762705629446970296352861004019084652585012933306375828775, 
9069697602289298897479257949144657270732090889455197964425043207, 
250127021374018898282936610542536017519164050047115725607341714968, 
6909145395201492293479975824651120370386436412105562027156097665318])],[[2, 10,
88, 1043, 14778, 236001, 4107925, 76314975, 1491934038, 30389576308, 
640286048416, 13877540824735, 308102204007536, 6983346070924707, 
161156356282624227, 3778249609096250059, 89826197363219012470, 
2162338803354415120414, 52637415804379149938876, 1294313658632145337351381, 
32118082448138745067175242, 803656789698224684452667975, 
20262539635339176715000960941, 514456553505357928725536149803, 
13146084523635788235064716197728, 337929024350121818044901686404816, 
8734691492940974137071498064995420, 226931194428057541769204674879130191, 
5923987397778903817189358328568041496, 155335609958542073698381974113868127891,
4090172312867860136825480052716884724147, 
108121976818168155620957000319917917053675, 
2868707794254575240567639311917494731749030, 
76377538885644568975349924729052848698617526, 
2040172740682907191699950846063214773112927416, 
54665344392211673342456683384055104205997175257, 
1469025374919143636369316715736858925903810273670, 
39586979783512218527277338099905807341274587256147, 
1069596920795621360143277142155882112468901055822299, 
28971834889893726116466068771262180074158013962368089, 
786624416885179957698948378595042627165085805977597238, 
21406496941578870323675397740377275998112856431253739940, 
583801369714608515305502011392156725334624008192909440168, 
15954513928133137501267139726262869284981213941344807489857, 
436879272160793629128022091511848928647620180950721848780592, 
11985652641165379506890719555297678340424492500261026978221269, 
329419762705629446970296352861004019084652585012933306375828775, 
9069697602289298897479257949144657270732090889455197964425043207, 
250127021374018898282936610542536017519164050047115725607341714968, 
6909145395201492293479975824651120370386436412105562027156097665318]])

;
> ope:=Findrec(A, n, N, 10)
Typesetting:-mprintslash([(ope := -(n-1)*(n-3)*(3*n+8)/(3*n+5)/(n+5)/(n+4)+(n+3
)*(9*n^2-3*n-16)/(3*n+5)/(n+5)/(n+4)*N-2*(3*n+7)*(15*n^2+65*n+62)/(3*n+5)/(n+5)
/(n+4)*N^2+N^3)],[-(n-1)*(n-3)*(3*n+8)/(3*n+5)/(n+5)/(n+4)+(n+3)*(9*n^2-3*n-16)
/(3*n+5)/(n+5)/(n+4)*N-2*(3*n+7)*(15*n^2+65*n+62)/(3*n+5)/(n+5)/(n+4)*N^2+N^3])

;
> SeqFromRec(ope, n, N, [2,10,88], 3000)[3000]
1055961597172638192205714533827955182069330710185887123715638338751912356623868\
934358954829265893265497184019516455497946501358614406592180916

;
> #The answer is 1055961597172638192205714533827955182069330710185887123715638338751912356623868\
> 934358954829265893265497184019516455497946501358614406592180916.
;
> 
;
> #Q4.
;
> #Use the appropriate procedures in ComboProject4.txt to find
> #Sum(binomial(3,k)^2*binomial(3+k,k)^2,k=0..3)
> #Don't do it directly! Use Z and then use SeqFromRec.
;
> read `ComboProject4.txt`
`----------------------------`
``
`Team Leader: tbd `
``
`Other Team members: tbd `
`-------------------------------------`
`This is ComboProject4.txt, a Maple package that is part of Project 4 in Dr. Z.\
's Combinatorics Class at Rutgers University`
`Its purpose is to generate a database of all binomial coefficients sum of the \
form`
`Sum (binomial(n,k)*binomial(a1*n+b1*k,k),k=0..n)*x^k  for all non-trivial a1, \
b1,x <=K for some fixed K `
``
Also
``
`Sum (binomial(n,k)*binomial(a1*n+b1*k,k)*binomial(a2*n+b2*k,k)*x^k,k=0..n)  fo\
r all non-trivial a1, b1,a2,b2,x <=K for some fixed K `
``
Also
``
`Sum (binomial(n,k)*binomial(a1*n+b1*k,k)*binomial(a2*n+b2*k,k),k=0..n)*binomia\
l(a3*n+b3*n)*x^k,k=0..n)`
`  for all non-trivial a1, b1,a2,b2,a3,b3,x <=K for some fixed K `
`It gives databases with thw  beginning part of each sequence, the recurrence (\
generated by the Zeilberger algorithm)`
`And growh constants and critical exponents. It also tries to investigate congr\
uence properties in the style of Gessel. `
``
`For a list of all the functions type: Help(); `
`For Help with any of the functions, type  Help(FunctionName):`

;
> ope:=Z(binomial(n,k)^2*binomial(n+k,k)^2, k, n, N)
Typesetting:-mprintslash([(ope := (n+1)^3-(17*n^2+51*n+39)*N*(2*n+3)+(n+2)^3*N^
2)],[(n+1)^3-(17*n^2+51*n+39)*N*(2*n+3)+(n+2)^3*N^2])

;
> binomial(1,0)^2*binomial(1,0)^2+binomial(1,1)^2*binomial(2,1)^2
5

;
> binomial(2,0)^2*binomial(2,0)^2+binomial(2,1)^2*binomial(3,1)^2+binomial(2,2)^2*binomial(4,2)^2
73

;
> SeqFromRec(ope, n, N, [5,73], 3000)[3000]
2722642711747329013359227913572710537967104475547733421085159876139384634676850\
735063904093083359261956322867579665053314255370804763722281790779

;
> #The answer is 2722642711747329013359227913572710537967104475547733421085159876139384634676850\
> 735063904093083359261956322867579665053314255370804763722281790779
;
> 
;
> #Q5.
;
> #Use the appropriate procedures in ComboProject5.txt to find the number of 3 by 101 TicTacToe boards that ended in a tie (i.e. had 151 X's and 150 O'x and no three consectutive Xs, or O's horizontally, vertically, or diagonally.
;
> read `ComboProject5.txt`
`This is ComboProject5.txt, a Maple package that is part of Project 5 in Dr. Z.\
's Combinatorics Class at Rutgers University`
`Its purpose is the generate and study sequences enumerating Final tie position\
s in a k by n generalized TicTacToe`
`in a k by n board, for fixed k. The classical case is k=3 and n=3.`
``
`Team Leader: tbd `
``
`Other Team members: tbd `
`For a list of all the functions type: Help(); `
`For Help with any of the functions, type  Help(FunctionName):`

;
> 
;
> 
;
> OddTTT3(50)[50]
1290808418002135615116

;
> #The answer is 1290808418002135615116.
;
> 
;
> #Q6.
;
> #Use the appropriate procedures in ComboProject6.txt to approxinate the average degree of an induced graph if you take 1000 random choices of 257 vetrices in Bn(9). Of coure it changses from run to run, but it should be close.
;
> read `ComboProject6.txt`
`This is ComboProject6.txt, a Maple package that is part of Project 6 in Dr. Z.\
's Combinatorics Class at Rutgers University`
`to generate and investigate minimal degrees             `
`and average degrees of vertices in induced subgraphs of famous families of gra\
phs`
`inspired by Hao Huang's amazing proof of the Sensitivity Conjecture `
``
`Team Leader: tbd `
``
`Other Team members: tbd `
``
`For a list of all the functions type: Help(); `
`For Help with any of the functions, type  Help(FunctionName):`

;
> SimuAvDegree(Bn(9)[1], 257, 1000)[1]
4505.214007782101167315175097276264591440

;
> #The answe is around 4505.21
;
> 
;
> #Q7.
;
> #Use the appropriate procedures in ComboProject7.txt to find the coefficient of x^2000 y^2000 in the bi-variate Taylor series of
> #1/(1-4*x-5*y+11*x*y)
> #Don't do it directly!
;
> read `ComboProject7.txt`
`----------------------`
``
`Team Leader: tbd `
``
`Other Team members: tbd `
`----------------------`
`This is ComboProject7.txt, a Maple package that is part of Project 2 in Dr. Z.\
's Combinatorics Class at Rutgers University`
`Its purpose is to create a database of integer sequences  that are in the diag\
onals of the Taylor`
`expansions of rational functions of the form 1/(1-a*x-b*y-c*x*y) with small co\
efficients, a,b,c`
`and analogously for two and three variables`
`For a list of all the functions type: Help(); `
`For Help with any of the functions, type  Help(FunctionName):`

;
> 
;
> L:=DiagSeq2(1/(1-4*x-5*y+11*x*y), x,y,40)
Typesetting:-mprintslash([(L := [29, 1201, 55709, 2718241, 136499549, 
6983136721, 361934838749, 18940867256641, 998610514846109, 52960778923772401, 
2822254149237600029, 150996060066161512801, 8105710040251853964509, 
436375297073794971041041, 23550703468724995335309149, 
1273753828387177058375214721, 69022838344180991405642469149, 
3746559405241737948202738305841, 203669815784776769428423626545309, 
11086861078996588534031451312880801, 604256993748942094521267163560744029, 
32969852600145475472865737962464440401, 
1800744588079572245064094558765973657309, 
98444157240260504657557313952020148219841, 
5386391406185083972748912501086569724782749, 
294949204388305814196405027477006756714948721, 
16162642214109917120059498092731149508026283549, 
886279117170311525411258722612100085396935171041, 
48629667202107605251794796170332010573377268588509, 
2669846905355182981438426312993073696379688701325201, 
146659144633215099583889065728594908726268058957032029, 
8060364421965521736762180812065808712742860356119584001, 
443209779617733321460845223280088785967641874151629934109, 
24381516666480809273633261201489227557210174119842101854641, 
1341829994750878413487149669017304545043047992672692578920349, 
73877006558597567391561230758842310542745853597653964406738721, 
4068989498038276318886083825898102508669877162436518750683481949, 
224192231575537096956979281347921998212029201098492933791779052241, 
12356718958876778025402474918421290940323002842565425844651281375709, 
681281999849543472391427120235558340867935842808340061388317007105601])],[[29,
1201, 55709, 2718241, 136499549, 6983136721, 361934838749, 18940867256641, 
998610514846109, 52960778923772401, 2822254149237600029, 150996060066161512801,
8105710040251853964509, 436375297073794971041041, 23550703468724995335309149, 
1273753828387177058375214721, 69022838344180991405642469149, 
3746559405241737948202738305841, 203669815784776769428423626545309, 
11086861078996588534031451312880801, 604256993748942094521267163560744029, 
32969852600145475472865737962464440401, 
1800744588079572245064094558765973657309, 
98444157240260504657557313952020148219841, 
5386391406185083972748912501086569724782749, 
294949204388305814196405027477006756714948721, 
16162642214109917120059498092731149508026283549, 
886279117170311525411258722612100085396935171041, 
48629667202107605251794796170332010573377268588509, 
2669846905355182981438426312993073696379688701325201, 
146659144633215099583889065728594908726268058957032029, 
8060364421965521736762180812065808712742860356119584001, 
443209779617733321460845223280088785967641874151629934109, 
24381516666480809273633261201489227557210174119842101854641, 
1341829994750878413487149669017304545043047992672692578920349, 
73877006558597567391561230758842310542745853597653964406738721, 
4068989498038276318886083825898102508669877162436518750683481949, 
224192231575537096956979281347921998212029201098492933791779052241, 
12356718958876778025402474918421290940323002842565425844651281375709, 
681281999849543472391427120235558340867935842808340061388317007105601]])

;
> ope:=Findrec(L, n, N,10)
Typesetting:-mprintslash([(ope := 121*(n+1)/(n+2)-29*(2*n+3)/(n+2)*N+N^2)],[121
*(n+1)/(n+2)-29*(2*n+3)/(n+2)*N+N^2])

;
> SeqFromRec(ope, n, N, [29,1201],2000)[2000]
7736468599157553450805928807119878681140000674112677110896454652973021857821404\
37651737245647882206781438666359768916791715657797616

;
> #The answer is 7736468599157553450805928807119878681140000674112677110896454652973021857821404\
> 37651737245647882206781438666359768916791715657797616

;
> 
;
> 
;
> 
;
> 
;
> 
;