Generating Functions for Enumerating the Number of Spanning Trees (and Sum o\ f the Leaves) in Friendship graphs where n people live in a one-sided ST\ RAIGHT street, and every one is friends with all the neighbors distance \ at most r as well as their asymptotics and the BZ constant for r from 2 to, 5 By Shalosh B. Ekhad Theorem number, 1 Part I: Let a(n) be the number of spanning trees of the graph, H[n, 2], whose vertice\ s are 1, ...,n, and where every vertex i is connected to i+1,..., min(n, i + 2), Then infinity ----- \ n 1 ) a[n + 2] x = ------------ / 2 ----- x - 3 x + 1 n = 0 and in Maple notation 1/(x^2-3*x+1) The asympotics is -2*5^(1/2)/(5*5^(1/2)-15)*(-2/(5^(1/2)-3))^n and in decimals 1.17082039324993690892275210061938287063218550788345771728126917362315627769134\ 1469824324322513634682490852452845232135051275980317334122159075908036460035812\ 6600334519575637497433829935967919569741607284051252601355010270177242193326259\ 2976172917577778816866288985522073220448353277267284954771141720*2.618033988749\ 8948482045868343656381177203091798057628621354486227052604628189024497072072041\ 8939113748475408807538689175212663386222353693179318006076672635443338908659593\ 9582905638322661319928290267880675208766892501711696207032221043216269548626296\ 31361443814975870122034080588795445474924618569536^n Part II: Let b(n) be the sum of the number of leaves in all spanning trees of the abo\ ve-mentioned graph, H[n, 2], Then infinity ----- 2 3 2 \ n 2 (x - x + 1) (x - x - 2 x + 1) ) b[n + 2] x = ---------------------------------- / 2 2 ----- (x - 3 x + 1) n = 0 and in Maple notation 2*(x^2-x+1)*(x^3-x^2-2*x+1)/(x^2-3*x+1)^2 The asympotics is (12*5^(1/2)-28)/(5*5^(1/2)-15)*(-2/(5^(1/2)-3))^n*(1+n) and in decimals 0.30557280900008412143633053250748950582375265615538971029164110183579162974\ 487804023423423664848709001219672953969048659829869291022117045456545595\ 138661891645328873072324833367548934187094405736778569545983298648599863\ 064303437422316542698436109896294910844948019303902372735528963643620060\ 3051443693 2.618033988749894848204586834365638117720309179805762862135448\ 622705260462818902449707207204189391137484754088075386891752126633862223\ 536931793180060766726354433389086595939582905638322661319928290267880675\ 208766892501711696207032221043216269548626296313614438149758701220340805\ n 88795445474924618569536 (1. + n) The BZ constant is -6+14/5*5^(1/2) and in decimals .260990336999411149945686272447573459233731406912272027958512287149458591785853\ 7183603603434605903699146228932221665938119091496284518068180418083402936675848\ 2697888493726166427157460690339159842550013178116909459800958549875938043784201\ 110947230725935624085363864872683390851297254494659577863989404 Theorem number, 2 Part I: Let a(n) be the number of spanning trees of the graph, H[n, 3], whose vertice\ s are 1, ...,n, and where every vertex i is connected to i+1,..., min(n, i + 3), Then infinity ----- 2 \ n 4 x + x + 3 ) a[n + 3] x = - ---------------------------------- / 4 3 2 ----- (x - 1) (x - 4 x - x - 4 x + 1) n = 0 and in Maple notation -(4*x^2+x+3)/(x-1)/(x^4-4*x^3-x^2-4*x+1) The asympotics is (-8*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^9+106*RootOf(_Z^4-4*_Z^3-_Z^2-4* _Z+1,index = 1)^8-352*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^7+173*RootOf(_Z ^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^6-110*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1 )^5+500*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^4+218*RootOf(_Z^4-4*_Z^3-_Z^2 -4*_Z+1,index = 1)^3+172*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^2+50*RootOf( _Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)+35)/(16*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^8-128*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^7+336*RootOf(_Z^4-4*_Z^3- _Z^2-4*_Z+1,index = 1)^6-336*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^5+196* RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^4-168*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1, index = 1)^3+84*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^2-16*RootOf(_Z^4-4*_Z ^3-_Z^2-4*_Z+1,index = 1)+16)*(-RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^3+4* RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^2+RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1, index = 1)+4)^n and in decimals 3.90352444042068690574392885294900364177011656020448352936235976515190331308368\ 7835498454541471464014382696565761430084432159251461306785330989222416391545656\ 1571139933622355761432002282808281740729876446902049218252531090574786751156453\ 7355293635077438795012721210885085810274144935941613347601588282*4.419480365787\ 5667074848413155156881333186325196333651926684832652318194029734233993516067056\ 2235617294200632046839265454646838409371545219466019855889276199478293020635623\ 0468040676060014431004669121124061629898241290300356640072093270969917949814978\ 61668038627041193408024058104919310419706116006054^n Part II: Let b(n) be the sum of the number of leaves in all spanning trees of the abo\ ve-mentioned graph, H[n, 3], Then infinity ----- \ n 12 11 10 9 8 7 ) b[n + 3] x = (32 x - 272 x + 452 x + 376 x + 816 x + 12 x / ----- n = 0 6 5 4 3 2 / 2 - 8 x - 232 x + 16 x - 40 x + 18 x - 24 x + 6) / ((x - 1) / 4 3 2 2 (x - 4 x - x - 4 x + 1) ) and in Maple notation (32*x^12-272*x^11+452*x^10+376*x^9+816*x^8+12*x^7-8*x^6-232*x^5+16*x^4-40*x^3+ 18*x^2-24*x+6)/(x-1)^2/(x^4-4*x^3-x^2-4*x+1)^2 The asympotics is (1593-21602*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^3-930*RootOf(_Z^4-4*_Z^3- _Z^2-4*_Z+1,index = 1)^2+173158*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^4+ 868040*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^6-729702*RootOf(_Z^4-4*_Z^3-_Z ^2-4*_Z+1,index = 1)^5+8896*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^26-211424 *RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^25+2116536*RootOf(_Z^4-4*_Z^3-_Z^2-4 *_Z+1,index = 1)^24-11576064*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^23+ 37801808*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^22-78132208*RootOf(_Z^4-4*_Z ^3-_Z^2-4*_Z+1,index = 1)^21+118037918*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1 )^20+108595129*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^12-39040336*RootOf(_Z^ 4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^11+44311752*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1, index = 1)^10-15580920*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^9+7484162* RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^8-5494152*RootOf(_Z^4-4*_Z^3-_Z^2-4* _Z+1,index = 1)^7-5166*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)-171374592* RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^19+231621834*RootOf(_Z^4-4*_Z^3-_Z^2-\ 4*_Z+1,index = 1)^18-228248066*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^17+ 228365970*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^16-238585902*RootOf(_Z^4-4* _Z^3-_Z^2-4*_Z+1,index = 1)^15+156567406*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^14-130357426*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^13)/(128-4032*RootOf( _Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^3+1472*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^2+9352*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^4+41328*RootOf(_Z^4-4*_Z^ 3-_Z^2-4*_Z+1,index = 1)^6-22624*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^5+ 102592*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^12-140672*RootOf(_Z^4-4*_Z^3- _Z^2-4*_Z+1,index = 1)^11+145152*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^10-\ 133312*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^9+106184*RootOf(_Z^4-4*_Z^3-_Z ^2-4*_Z+1,index = 1)^8-68576*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^7-256* RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)+128*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1, index = 1)^16-2048*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^15+13568*RootOf(_Z ^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^14-48384*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^13)*(-RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^3+4*RootOf(_Z^4-4*_Z^3-_Z^ 2-4*_Z+1,index = 1)^2+RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)+4)^n*(1+n) and in decimals 1.21364320047905924642315881530296461130170174296989655686087614232214822164\ 217445323584888826549555670434766972319358517666538882384551562348398576\ 043345182729809827278906139568292405414109317456172025541570068241768596\ 536654372015603040149750237124080672548659148010878189269846341986031375\ 390533257 4.4194803657875667074848413155156881333186325196333651926684832\ 652318194029734233993516067056223561729420063204683926545464683840937154\ 521946601985588927619947829302063562304680406760600144310046691211240616\ 298982412903003566400720932709699179498149786166803862704119340802405810\ n 4919310419706116006054 (1. + n) The BZ constant is -5931532928/6561*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^12+1165217368960/ 137781*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^11-2939512673528/137781*RootOf (_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^10+196836144328/19683*RootOf(_Z^4-4*_Z^3-_Z ^2-4*_Z+1,index = 1)^9-589535458720/19683*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^8+2907925389122/45927*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^7+ 241205765102/6561*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^6+196080412880/2187 *RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)^5+4141878810841/137781*RootOf(_Z^4-4 *_Z^3-_Z^2-4*_Z+1,index = 1)^4+2584470791912/137781*RootOf(_Z^4-4*_Z^3-_Z^2-4* _Z+1,index = 1)^3-500776872826/137781*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1) ^2-495038589448/137781*RootOf(_Z^4-4*_Z^3-_Z^2-4*_Z+1,index = 1)+4219524400/ 6561 and in decimals .310909594394204344008503510728871359457534156622455497862965574296392568706818\ 2389717542663389754515614209307854901398957824822098178113415350516967063041587\ 8171787527146830199727656701613986631861076178492467710995347917371238944954205\ 2891443925255860750442024536049386427251672816518078123144 Theorem number, 3 Part I: Let a(n) be the number of spanning trees of the graph, H[n, 4], whose vertice\ s are 1, ...,n, and where every vertex i is connected to i+1,..., min(n, i + 4), Then infinity ----- \ n 10 9 8 7 6 5 ) a[n + 4] x = (36 x + 20 x - 76 x + 103 x - 49 x - 608 x / ----- n = 0 4 3 2 / - 112 x + 112 x + 5 x + 13 x + 16) / ( / 6 5 4 3 2 (x - 3 x + 6 x - 10 x + 6 x - 3 x + 1) 8 7 6 5 4 3 2 (x - 4 x - 17 x + 8 x + 49 x + 8 x - 17 x - 4 x + 1)) and in Maple notation (36*x^10+20*x^9-76*x^8+103*x^7-49*x^6-608*x^5-112*x^4+112*x^3+5*x^2+13*x+16)/(x ^6-3*x^5+6*x^4-10*x^3+6*x^2-3*x+1)/(x^8-4*x^7-17*x^6+8*x^5+49*x^4+8*x^3-17*x^2-\ 4*x+1) The asympotics is (284+267*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)-19634514*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1, index = 1)^10-276920*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4 *_Z+1,index = 1)^9-2285256*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17* _Z^2-4*_Z+1,index = 1)^23+1740798*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8* _Z^3-17*_Z^2-4*_Z+1,index = 1)^22+12271061*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49 *_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^21-11975786*RootOf(_Z^8-4*_Z^7-17*_Z^6+8 *_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^20-21997992*RootOf(_Z^8-4*_Z^7-\ 17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^19+34637888*RootOf(_Z^8 -4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^18-1587374* RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^17-\ 59145498*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^16+48140808*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+ 1,index = 1)^15+48663456*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z ^2-4*_Z+1,index = 1)^14-46807506*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z ^3-17*_Z^2-4*_Z+1,index = 1)^13+2804092*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z ^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^12+14912696*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z ^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^11+14004*RootOf(_Z^8-4*_Z^7-17*_Z^6 +8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^28+61332*RootOf(_Z^8-4*_Z^7-17 *_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^27-161872*RootOf(_Z^8-4* _Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^26-40311*RootOf(_Z ^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^25+349074* RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^24+ 8539064*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^8-592434*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1, index = 1)^7-1237134*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4 *_Z+1,index = 1)^6+74367*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z ^2-4*_Z+1,index = 1)^5-19314*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-\ 17*_Z^2-4*_Z+1,index = 1)^4-1714*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z ^3-17*_Z^2-4*_Z+1,index = 1)^3+11826*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+ 8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^2+432*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^ 4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^30-5824*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49 *_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^29)/(16+176*RootOf(_Z^8-4*_Z^7-17*_Z^6+8 *_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)+582868*RootOf(_Z^8-4*_Z^7-17*_Z^ 6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^10+14216*RootOf(_Z^8-4*_Z^7-\ 17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^9-1552*RootOf(_Z^8-4*_Z ^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^23-12620*RootOf(_Z^8 -4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^22+35576*RootOf (_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^21-52892* RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^20-\ 45328*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1 )^19+284200*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1, index = 1)^18-307960*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4 *_Z+1,index = 1)^17-3752*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z ^2-4*_Z+1,index = 1)^16+753224*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3 -17*_Z^2-4*_Z+1,index = 1)^15-1434860*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4 +8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^14+203288*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+ 49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^13+1543624*RootOf(_Z^8-4*_Z^7-17*_Z^6+ 8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^12-1366504*RootOf(_Z^8-4*_Z^7-\ 17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^11+64*RootOf(_Z^8-4*_Z^ 7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^26-832*RootOf(_Z^8-4* _Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^25+3184*RootOf(_Z^ 8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^24-289448* RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^8+ 165128*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^7-29720*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1, index = 1)^6-8464*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z +1,index = 1)^5+12868*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-\ 4*_Z+1,index = 1)^4-4168*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z ^2-4*_Z+1,index = 1)^3-332*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17* _Z^2-4*_Z+1,index = 1)^2)*(-RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17 *_Z^2-4*_Z+1,index = 1)^7+4*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17 *_Z^2-4*_Z+1,index = 1)^6+17*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-\ 17*_Z^2-4*_Z+1,index = 1)^5-8*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-\ 17*_Z^2-4*_Z+1,index = 1)^4-49*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3 -17*_Z^2-4*_Z+1,index = 1)^3-8*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3 -17*_Z^2-4*_Z+1,index = 1)^2+17*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^ 3-17*_Z^2-4*_Z+1,index = 1)+4)^n and in decimals 22.8362649504052577281914842828321378967389271701504248140234316887942902081234\ 7290691076113386367136933759580535126599419403679340008886093103421903102328275\ 7451729674322624596670223528379154112580879327429630552553977310234416167540654\ 5557313903967868834321861804099112984858812614027410530821227387*6.298096056225\ 7735736763280347455186344983566539488734555762957580607021719381702047684955966\ 0868174082297905849451741105870880197908448107777793195646538809910654441251005\ 5905938348446142400780573792080060295441158235077834737768247256185377889131512\ 94989027077865744774017135367553226025262757348097^n Part II: Let b(n) be the sum of the number of leaves in all spanning trees of the abo\ ve-mentioned graph, H[n, 4], Then infinity ----- \ n 31 30 29 28 ) b[n + 4] x = (2016 x - 26424 x + 76784 x + 177840 x / ----- n = 0 27 26 25 24 23 - 805992 x + 336572 x + 1406432 x - 6628092 x + 9345048 x 22 21 20 19 18 + 17151224 x - 35171192 x + 20561596 x + 9552176 x - 140184504 x 17 16 15 14 13 + 76273480 x + 138809200 x - 6890160 x - 26763408 x - 13830680 x 12 11 10 9 8 - 8491192 x + 1139888 x + 2000920 x + 599424 x + 149240 x 7 6 5 4 3 2 - 31696 x - 9420 x - 3120 x - 2644 x + 976 x - 144 x - 184 x + 36) / 6 5 4 3 2 2 / ((x - 3 x + 6 x - 10 x + 6 x - 3 x + 1) / 8 7 6 5 4 3 2 2 (x - 4 x - 17 x + 8 x + 49 x + 8 x - 17 x - 4 x + 1) ) and in Maple notation (2016*x^31-26424*x^30+76784*x^29+177840*x^28-805992*x^27+336572*x^26+1406432*x^ 25-6628092*x^24+9345048*x^23+17151224*x^22-35171192*x^21+20561596*x^20+9552176* x^19-140184504*x^18+76273480*x^17+138809200*x^16-6890160*x^15-26763408*x^14-\ 13830680*x^13-8491192*x^12+1139888*x^11+2000920*x^10+599424*x^9+149240*x^8-\ 31696*x^7-9420*x^6-3120*x^5-2644*x^4+976*x^3-144*x^2-184*x+36)/(x^6-3*x^5+6*x^4 -10*x^3+6*x^2-3*x+1)^2/(x^8-4*x^7-17*x^6+8*x^5+49*x^4+8*x^3-17*x^2-4*x+1)^2 The asympotics is (15531-79460*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1, index = 1)+108296372859*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^ 2-4*_Z+1,index = 1)^10+5776652130*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8* _Z^3-17*_Z^2-4*_Z+1,index = 1)^9+78185009961683944*RootOf(_Z^8-4*_Z^7-17*_Z^6+8 *_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^51-1119948579792053*RootOf(_Z^8-\ 4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^50-\ 240259853059614134*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4* _Z+1,index = 1)^49+326884287102482522*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4 +8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^48+103344184803982738*RootOf(_Z^8-4*_Z^7-17* _Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^47-1054693818163325795* RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^46+ 1322192143346643996*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4* _Z+1,index = 1)^45+1135495243359276802*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^ 4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^44-4026694427070706946*RootOf(_Z^8-4*_Z^7-17 *_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^43+1924555181020773947* RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^42+ 4355921321929132396*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4* _Z+1,index = 1)^41-8728797691613385605*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^ 4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^40+2192182470641470132*RootOf(_Z^8-4*_Z^7-17 *_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^39+13909427463794003644* RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^38-\ 11962493163016363532*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4 *_Z+1,index = 1)^37-10900218509606834802*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49* _Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^36+14291236662527169624*RootOf(_Z^8-4*_Z^ 7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^35+ 2357488345915138772*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4* _Z+1,index = 1)^34-7357357727806232840*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^ 4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^33+2909521080955157624*RootOf(_Z^8-4*_Z^7-17 *_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^32-4064661812427398* RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^23+ 38455599669461101*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z +1,index = 1)^22+427202284486052*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z ^3-17*_Z^2-4*_Z+1,index = 1)^21-4451431332136046*RootOf(_Z^8-4*_Z^7-17*_Z^6+8* _Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^20-846857867869238*RootOf(_Z^8-4* _Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^19-542496883851282 *RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^18+ 171609341691490*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1 ,index = 1)^17+236669925347683*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3 -17*_Z^2-4*_Z+1,index = 1)^16+3578014362068*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+ 49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^15-27602402905248*RootOf(_Z^8-4*_Z^7-\ 17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^14-4260358749720*RootOf (_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^13+ 705042332212*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1, index = 1)^12+358491664560*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17* _Z^2-4*_Z+1,index = 1)^11+879665507816781172*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+ 49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^28-605708103481674708*RootOf(_Z^8-4*_Z ^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^27+19152201124553672 *RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^26+ 112066290484541744*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4* _Z+1,index = 1)^25-113592763763821154*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4 +8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^24+584304377588604296*RootOf(_Z^8-4*_Z^7-17* _Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^31-8719783550*RootOf(_Z^8-\ 4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^8+2765952*RootOf (_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^71-\ 92995488*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^70+1220241024*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4* _Z+1,index = 1)^69-7080287792*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-\ 17*_Z^2-4*_Z+1,index = 1)^68+6375362392*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z ^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^67+131797894902*RootOf(_Z^8-4*_Z^7-17*_Z^6+ 8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^66-557043227720*RootOf(_Z^8-4* _Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^65-256043444138* RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^64+ 6345943737222*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1, index = 1)^63-10404620845153*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-\ 17*_Z^2-4*_Z+1,index = 1)^62-22107545511756*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+ 49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^61+102787706051112*RootOf(_Z^8-4*_Z^7-\ 17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^60-111638278047166* RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^59-\ 317888362052938*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1 ,index = 1)^58+1359488189927786*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^ 3-17*_Z^2-4*_Z+1,index = 1)^57-894527373363185*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^ 5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^56-4492975151865804*RootOf(_Z^8-4*_Z ^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^55+10747322149717548 *RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^54-\ 3816783999335968*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+ 1,index = 1)^53-33162327065715340*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8* _Z^3-17*_Z^2-4*_Z+1,index = 1)^52-1474912342*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+ 49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^7+243419941*RootOf(_Z^8-4*_Z^7-17*_Z^6 +8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^6+53653596*RootOf(_Z^8-4*_Z^7-\ 17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^5-6785046*RootOf(_Z^8-4 *_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^4-2696126*RootOf( _Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^3+376985* RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^2-\ 2704345669385318214*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4* _Z+1,index = 1)^30+1205073332359026516*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^ 4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^29)/(64+1408*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z ^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)-463473088*RootOf(_Z^8-4*_Z^7-17*_Z^ 6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^10-45289840*RootOf(_Z^8-4*_Z^ 7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^9-26624*RootOf(_Z^8-4 *_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^51+274944*RootOf( _Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^50-1374208* RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^49+ 2776256*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^48+3917568*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1, index = 1)^47-35981024*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2 -4*_Z+1,index = 1)^46+86982688*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3 -17*_Z^2-4*_Z+1,index = 1)^45-44044092*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^ 4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^44-383684464*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z ^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^43+1265773688*RootOf(_Z^8-4*_Z^7-17 *_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^42-1339970736*RootOf(_Z^8 -4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^41-2026458476* RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^40+ 10002772624*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1, index = 1)^39-15360584448*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17* _Z^2-4*_Z+1,index = 1)^38-2365172512*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+ 8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^37+52610371304*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z ^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^36-94017224304*RootOf(_Z^8-4*_Z^7-\ 17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^35+39900896296*RootOf( _Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^34+ 170531020672*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1, index = 1)^33-393828265032*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17* _Z^2-4*_Z+1,index = 1)^32-1111772396256*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z ^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^23+1191284505992*RootOf(_Z^8-4*_Z^7-17*_Z^6 +8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^22-548909643952*RootOf(_Z^8-4* _Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^21-112694068716* RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^20+ 337338021136*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1, index = 1)^19-231752880584*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17* _Z^2-4*_Z+1,index = 1)^18+64010524032*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4 +8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^17+29052857528*RootOf(_Z^8-4*_Z^7-17*_Z^6+8* _Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^16-38738918656*RootOf(_Z^8-4*_Z^7 -17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^15+17405985192*RootOf( _Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^14-\ 1987784432*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1, index = 1)^13-2574596120*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z ^2-4*_Z+1,index = 1)^12+1829418720*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8* _Z^3-17*_Z^2-4*_Z+1,index = 1)^11+892096652884*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^ 5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^28+352037398096*RootOf(_Z^8-4*_Z^7-\ 17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^27-1659351076344*RootOf (_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^26+ 1425946528672*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1, index = 1)^25+14656505128*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17* _Z^2-4*_Z+1,index = 1)^24+260345730944*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^ 4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^31+76184532*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^ 5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^8+1024*RootOf(_Z^8-4*_Z^7-17*_Z^6+8* _Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^52-26706224*RootOf(_Z^8-4*_Z^7-17 *_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^7+1224376*RootOf(_Z^8-4* _Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^6+1756560*RootOf( _Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^5-236284* RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^4-\ 62560*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1 )^3+5088*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^2+350038769912*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-4* _Z+1,index = 1)^30-992406938352*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^ 3-17*_Z^2-4*_Z+1,index = 1)^29)*(-RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8* _Z^3-17*_Z^2-4*_Z+1,index = 1)^7+4*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8* _Z^3-17*_Z^2-4*_Z+1,index = 1)^6+17*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8 *_Z^3-17*_Z^2-4*_Z+1,index = 1)^5-8*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8 *_Z^3-17*_Z^2-4*_Z+1,index = 1)^4-49*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+ 8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^3-8*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+ 8*_Z^3-17*_Z^2-4*_Z+1,index = 1)^2+17*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4 +8*_Z^3-17*_Z^2-4*_Z+1,index = 1)+4)^n*(1+n) and in decimals 7.54183968047861397010472399332927094262603687549895250260964949220026463503\ 088054781408709274774234552611570947574783570525266729728911178306084677\ 741043668724324946776575634005245773887478200609253241892421612376258020\ 701620237573958880962412464229917475488818345618034146223205385634740799\ 712054502 6.2980960562257735736763280347455186344983566539488734555762957\ 580607021719381702047684955966086817408229790584945174110587088019790844\ 810777779319564653880991065444125100559059383484461424007805737920800602\ 954411582350778347377682472561853778891315129498902707786574477401713536\ n 7553226025262757348097 (1. + n) The BZ constant is 252717838089895965691933610993121094338363197083624757820586400423152/ 48119544464118580810546875*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17* _Z^2-4*_Z+1,index = 1)+ 53962065928713038889109345716363253247593107799083831183948398642023524992/ 6874220637731225830078125*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17* _Z^2-4*_Z+1,index = 1)^10+ 12077594577465792993541675472726005044823546803969996971418475003520326864/ 48119544464118580810546875*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17* _Z^2-4*_Z+1,index = 1)^9-\ 9254138623853692842403321147108410521599037496647029859579643669906236552/ 48119544464118580810546875*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17* _Z^2-4*_Z+1,index = 1)^23+ 16024493847161826089280226697001394837682709343036960840548825579562154192/ 48119544464118580810546875*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17* _Z^2-4*_Z+1,index = 1)^22+ 89140243547711530300598421462830420824440231014261647485772600306390156096/ 48119544464118580810546875*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17* _Z^2-4*_Z+1,index = 1)^21+ 6348533073040413699696636767440562936434401669356571770148008371801926544/ 6874220637731225830078125*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17* _Z^2-4*_Z+1,index = 1)^20-\ 302091525949218857910502954867250132196722123962764285604355223429894099368/ 48119544464118580810546875*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17* _Z^2-4*_Z+1,index = 1)^19-\ 484764349091960450921204637602966866554622049297658857761267517832845040832/ 48119544464118580810546875*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17* _Z^2-4*_Z+1,index = 1)^18+ 10197521734156558559764956189427847586214061297298324345224978141696599208/ 1924781778564743232421875*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17* _Z^2-4*_Z+1,index = 1)^17+ 401589878917872861201138499263268215446716079730304896129542294553381067408/ 16039848154706193603515625*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17* _Z^2-4*_Z+1,index = 1)^16+ 219907514291756288046800778192217236971439268707292945197242917129679990408/ 16039848154706193603515625*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17* _Z^2-4*_Z+1,index = 1)^15-\ 937896750321099251844294076876335240269030209099787958523855947100374602704/ 48119544464118580810546875*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17* _Z^2-4*_Z+1,index = 1)^14-\ 1336725706824518822138376631678274714064276705136881204606814658222917748408/ 48119544464118580810546875*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17* _Z^2-4*_Z+1,index = 1)^13-\ 266178368940210143782853168248983972746166865999663835976928180218000364288/ 48119544464118580810546875*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17* _Z^2-4*_Z+1,index = 1)^12+ 530846514473783062455639102414549989650857491833638691472364062715043005056/ 48119544464118580810546875*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17* _Z^2-4*_Z+1,index = 1)^11-\ 18631950019309493377541011485902214428179242913122759781602739328/ 293367135888544921875*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z^2-\ 4*_Z+1,index = 1)^28+ 17096734193155345341580946458103563684240356056883240330477309430432/ 118813690034860693359375*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17*_Z ^2-4*_Z+1,index = 1)^27+ 35031095765268112205830970941216423566129433682194099145366628686476928/ 9623908892823716162109375*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17* _Z^2-4*_Z+1,index = 1)^26+ 25440751158388116076677526619894449788022924902219323343047264719344376/ 16039848154706193603515625*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17* _Z^2-4*_Z+1,index = 1)^25-\ 1210785455064489369869306580066737305746944707702568526234199522469392096/ 16039848154706193603515625*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17* _Z^2-4*_Z+1,index = 1)^24+ 42773533161155764575300758405764304444160199465819263847466663062304/ 6874220637731225830078125-\ 16186173679444633096765210302400955886221323125676550677344912549464294896/ 9623908892823716162109375*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17* _Z^2-4*_Z+1,index = 1)^8-\ 3348616654289200962364962842014529529507298674187917145155329164317165688/ 5346616051568731201171875*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17* _Z^2-4*_Z+1,index = 1)^7+ 37124356772902602629882357710782670334582207146136843354844513813601216/ 1782205350522910400390625*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17* _Z^2-4*_Z+1,index = 1)^6+ 2805804766342955508160962850985673807908791147868360878027761861015286768/ 48119544464118580810546875*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17* _Z^2-4*_Z+1,index = 1)^5+ 429063416699392211449789997754700425238351346691868893406725502870630496/ 48119544464118580810546875*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17* _Z^2-4*_Z+1,index = 1)^4-\ 70745816221775156530409569309580793962230660618453318178385217687682528/ 48119544464118580810546875*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17* _Z^2-4*_Z+1,index = 1)^3-\ 20794809027320971082979553474901321454532971683238473090296601052891872/ 48119544464118580810546875*RootOf(_Z^8-4*_Z^7-17*_Z^6+8*_Z^5+49*_Z^4+8*_Z^3-17* _Z^2-4*_Z+1,index = 1)^2 and in decimals .330257145678491294152201301215982579594511047966878645657116548401719850150894\ 8011993845958733621898749861243663556491188833571288442784842579638132249880330\ 3136653393885225076822939108298232248635475703397612277447225929476675876480347\ 16152337916220601264 Theorem number, 4 Part I: Let a(n) be the number of spanning trees of the graph, H[n, 5], whose vertice\ s are 1, ...,n, and where every vertex i is connected to i+1,..., min(n, i + 5), Then infinity ----- \ n 36 35 34 33 32 ) a[n + 5] x = - (576 x + 1072 x + 880 x + 9397 x + 37352 x / ----- n = 0 31 30 29 28 27 - 38820 x - 162696 x - 409945 x - 940188 x - 6830079 x 26 25 24 23 22 - 10208568 x - 12657852 x - 11172468 x - 10598248 x + 2897948 x 21 20 19 18 17 + 13501001 x + 22499688 x + 26110019 x + 28239293 x + 18386448 x 16 15 14 13 12 + 10158616 x + 2700085 x - 4176485 x - 10893240 x - 8747319 x 11 10 9 8 7 - 7446180 x - 6025584 x - 4322484 x - 802676 x - 189560 x 6 5 4 3 2 / - 61343 x + 7796 x + 19551 x + 5928 x + 1012 x + 296 x + 125) / ( / 8 7 6 5 4 3 2 16 15 (x - 1) (x + 3 x + 6 x - x + 15 x - x + 6 x + 3 x + 1) (x - 5 x 14 13 12 11 10 9 8 7 + 10 x - 10 x - 28 x + 10 x + 110 x + 110 x + 88 x + 110 x 6 5 4 3 2 16 15 14 + 110 x + 10 x - 28 x - 10 x + 10 x - 5 x + 1) (x - 5 x - 23 x 13 12 11 10 9 8 7 6 - 10 x - 94 x - 485 x + 242 x + 110 x + 649 x + 110 x + 242 x 5 4 3 2 - 485 x - 94 x - 10 x - 23 x - 5 x + 1)) and in Maple notation -(576*x^36+1072*x^35+880*x^34+9397*x^33+37352*x^32-38820*x^31-162696*x^30-\ 409945*x^29-940188*x^28-6830079*x^27-10208568*x^26-12657852*x^25-11172468*x^24-\ 10598248*x^23+2897948*x^22+13501001*x^21+22499688*x^20+26110019*x^19+28239293*x ^18+18386448*x^17+10158616*x^16+2700085*x^15-4176485*x^14-10893240*x^13-8747319 *x^12-7446180*x^11-6025584*x^10-4322484*x^9-802676*x^8-189560*x^7-61343*x^6+ 7796*x^5+19551*x^4+5928*x^3+1012*x^2+296*x+125)/(x-1)/(x^8+3*x^7+6*x^6-x^5+15*x ^4-x^3+6*x^2+3*x+1)/(x^16-5*x^15+10*x^14-10*x^13-28*x^12+10*x^11+110*x^10+110*x ^9+88*x^8+110*x^7+110*x^6+10*x^5-28*x^4-10*x^3+10*x^2-5*x+1)/(x^16-5*x^15-23*x^ 14-10*x^13-94*x^12-485*x^11+242*x^10+110*x^9+649*x^8+110*x^7+242*x^6-485*x^5-94 *x^4-10*x^3-23*x^2-5*x+1) The asympotics is (125+576*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+ 110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1, index = 1)^36+1072*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+ 242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-\ 5*_Z+1,index = 1)^35+880*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z ^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23* _Z^2-5*_Z+1,index = 1)^34+9397*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-\ 485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^ 3-23*_Z^2-5*_Z+1,index = 1)^33+37352*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94* _Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-\ 10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^32-38820*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^ 13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94 *_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^31-162696*RootOf(_Z^16-5*_Z^15-23*_Z^14 -10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485* _Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^30-409945*RootOf(_Z^16-5*_Z^15-\ 23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242* _Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^29-940188*RootOf(_Z^16-\ 5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z ^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^28-6830079* RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^ 27-10208568*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10 +110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1, index = 1)^26-12657852*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^ 11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z ^2-5*_Z+1,index = 1)^25-11172468*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^ 12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10* _Z^3-23*_Z^2-5*_Z+1,index = 1)^24-10598248*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^ 13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94 *_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^23+2897948*RootOf(_Z^16-5*_Z^15-23*_Z^ 14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-\ 485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^22+13501001*RootOf(_Z^16-5* _Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7 +242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^21+22499688*RootOf (_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8 +110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^20+ 26110019*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+ 110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1, index = 1)^19+28239293*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^ 11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z ^2-5*_Z+1,index = 1)^18+18386448*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^ 12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10* _Z^3-23*_Z^2-5*_Z+1,index = 1)^17+10158616*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^ 13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94 *_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^16+2700085*RootOf(_Z^16-5*_Z^15-23*_Z^ 14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-\ 485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^15-4176485*RootOf(_Z^16-5*_Z ^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+ 242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^14-10893240*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^13-8747319 *RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^ 12-7446180*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+ 110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1, index = 1)^11-6025584*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11 +242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2 -5*_Z+1,index = 1)^10-4322484*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-\ 485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^ 3-23*_Z^2-5*_Z+1,index = 1)^9-802676*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94* _Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-\ 10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^8-189560*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^ 13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94 *_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^7-61343*RootOf(_Z^16-5*_Z^15-23*_Z^14-\ 10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485* _Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^6+7796*RootOf(_Z^16-5*_Z^15-23* _Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6 -485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^5+296*RootOf(_Z^16-5*_Z^15-\ 23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242* _Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)+19551*RootOf(_Z^16-5*_Z ^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+ 242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^4+5928*RootOf(_Z^16 -5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110* _Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^3+1012*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^2)/(-4824* RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^ 36+29933*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+ 110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1, index = 1)^35+40838*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+ 242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-\ 5*_Z+1,index = 1)^34-58190*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485* _Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23 *_Z^2-5*_Z+1,index = 1)^33-76318*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^ 12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10* _Z^3-23*_Z^2-5*_Z+1,index = 1)^32+814341*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13 -94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94* _Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^31-3035267*RootOf(_Z^16-5*_Z^15-23*_Z^14 -10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485* _Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^30-1109003*RootOf(_Z^16-5*_Z^15-\ 23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242* _Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^29-2959106*RootOf(_Z^16 -5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110* _Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^28-507191* RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^ 27-4645363*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+ 110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1, index = 1)^26+6046366*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11 +242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2 -5*_Z+1,index = 1)^25+3564357*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-\ 485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^ 3-23*_Z^2-5*_Z+1,index = 1)^24+7227213*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-\ 94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z ^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^23+3233098*RootOf(_Z^16-5*_Z^15-23*_Z^14-\ 10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485* _Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^22+7796569*RootOf(_Z^16-5*_Z^15-\ 23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242* _Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^21-3687255*RootOf(_Z^16 -5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110* _Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^20-1291638* RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^ 19-6450307*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+ 110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1, index = 1)^18-2222763*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11 +242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2 -5*_Z+1,index = 1)^17-6045410*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-\ 485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^ 3-23*_Z^2-5*_Z+1,index = 1)^16+1607933*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-\ 94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z ^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^15-1114087*RootOf(_Z^16-5*_Z^15-23*_Z^14-\ 10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485* _Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^14+1757630*RootOf(_Z^16-5*_Z^15-\ 23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242* _Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^13+162917*RootOf(_Z^16-\ 5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z ^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^12+1386429* RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^ 11-479611*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+ 110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1, index = 1)^10+40546*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+ 242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-\ 5*_Z+1,index = 1)^9-13502*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485* _Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23 *_Z^2-5*_Z+1,index = 1)^8-1978*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-\ 485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^ 3-23*_Z^2-5*_Z+1,index = 1)^7-7651*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z ^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10 *_Z^3-23*_Z^2-5*_Z+1,index = 1)^6+1000*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-\ 94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z ^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^5+5*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13 -94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94* _Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)+364*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^ 13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94 *_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^4-93*RootOf(_Z^16-5*_Z^15-23*_Z^14-10* _Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5 -94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^3+31*RootOf(_Z^16-5*_Z^15-23*_Z^14-\ 10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485* _Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^2+16*RootOf(_Z^16-5*_Z^15-23*_Z^ 14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-\ 485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^41-123*RootOf(_Z^16-5*_Z^15-\ 23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242* _Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^40-49*RootOf(_Z^16-5*_Z ^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+ 242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^39+419*RootOf(_Z^16 -5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110* _Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^38-276*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^37)*(1/ RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1))^ n and in decimals 194.678094852967184875601993571069359907375209042413772215025409112573627014652\ 3972593080764502034494900121097687671652165572051004739595064980606739366842186\ 1062706435920216383563776226326567439358647016945324278356900653340105125107179\ 5810664178845416144727987284388548896566189456823153531782198281*8.216271114701\ 8080784197270517005864370282025075930083403333260117064480028303210164396856662\ 1743991959463897966104229258622840833148397780121598105156859723905359918565442\ 5456249668868065723070529646912028862036409706909970198249278968640386785790148\ 21722529481650260900175511656134298623976970864339^n Part II: Let b(n) be the sum of the number of leaves in all spanning trees of the abo\ ve-mentioned graph, H[n, 5], Then infinity ----- \ n 86 85 84 83 ) b[n + 5] x = (286720 x - 4407200 x + 12552832 x + 51804128 x / ----- n = 0 82 81 80 79 - 140078160 x - 223042112 x + 3392556960 x - 6772574688 x 78 77 76 75 - 32998308048 x + 37874334944 x + 159383937616 x - 1048771754582 x 74 73 72 + 1215139671232 x + 8239060471446 x - 1765281505312 x 71 70 69 - 31306266572154 x + 140453959471792 x - 109339756667154 x 68 67 66 - 756837798553936 x - 727369523814740 x + 2864334083478544 x 65 64 63 - 10477687896754602 x + 11279194115203312 x + 15663965414461944 x 62 61 60 + 50243800946136208 x + 7585150625375352 x + 83669848441900164 x 59 58 57 - 54080107834236800 x - 101534367824757412 x - 318108985457311982 x 56 55 54 - 224696925497309220 x - 429754497077154194 x - 24249322681081988 x 53 52 51 + 197334828968756032 x + 845234595728857624 x + 859162871503526066 x 50 49 + 1326621361070739180 x + 653400209972170158 x 48 47 + 184838822003090368 x - 988422155012723648 x 46 45 - 1328611424340516992 x - 2177738311926879038 x 44 43 - 1596665204326268112 x - 1105428881624370722 x 42 41 + 185590541186208052 x + 776623498697357200 x 40 39 + 1788809753262611180 x + 1610816195760422306 x 38 37 + 1401845678707693904 x + 577974837834111886 x 36 35 34 + 119759331037872964 x - 611599022007774384 x - 690592798199163780 x 33 32 31 - 708917213285279822 x - 440606003342926672 x - 276442108433622098 x 30 29 28 + 5593730558339024 x + 88017606988549760 x + 120986611230999088 x 27 26 25 + 93058401778691618 x + 71699199535821380 x + 28745246203186526 x 24 23 22 + 7558736132415480 x + 1959786699784544 x + 15320630140164 x 21 20 19 - 592380205488542 x - 286638698161740 x - 88033161671554 x 18 17 16 - 28497194371004 x - 6453784987872 x + 617443648412 x 15 14 13 12 + 684261616584 x + 260166304016 x + 87564069752 x + 22059801984 x 11 10 9 8 7 + 2826671114 x + 237136688 x - 65794300 x - 34020480 x - 6653454 x 6 5 4 3 2 - 1109280 x - 610662 x - 66432 x + 3114 x - 3840 x - 1370 x + 320) / 2 8 7 6 5 4 3 2 2 16 / ((x - 1) (x + 3 x + 6 x - x + 15 x - x + 6 x + 3 x + 1) (x / 15 14 13 12 11 10 9 8 - 5 x + 10 x - 10 x - 28 x + 10 x + 110 x + 110 x + 88 x 7 6 5 4 3 2 2 16 15 + 110 x + 110 x + 10 x - 28 x - 10 x + 10 x - 5 x + 1) (x - 5 x 14 13 12 11 10 9 8 7 - 23 x - 10 x - 94 x - 485 x + 242 x + 110 x + 649 x + 110 x 6 5 4 3 2 2 + 242 x - 485 x - 94 x - 10 x - 23 x - 5 x + 1) ) and in Maple notation (286720*x^86-4407200*x^85+12552832*x^84+51804128*x^83-140078160*x^82-223042112* x^81+3392556960*x^80-6772574688*x^79-32998308048*x^78+37874334944*x^77+ 159383937616*x^76-1048771754582*x^75+1215139671232*x^74+8239060471446*x^73-\ 1765281505312*x^72-31306266572154*x^71+140453959471792*x^70-109339756667154*x^ 69-756837798553936*x^68-727369523814740*x^67+2864334083478544*x^66-\ 10477687896754602*x^65+11279194115203312*x^64+15663965414461944*x^63+ 50243800946136208*x^62+7585150625375352*x^61+83669848441900164*x^60-\ 54080107834236800*x^59-101534367824757412*x^58-318108985457311982*x^57-\ 224696925497309220*x^56-429754497077154194*x^55-24249322681081988*x^54+ 197334828968756032*x^53+845234595728857624*x^52+859162871503526066*x^51+ 1326621361070739180*x^50+653400209972170158*x^49+184838822003090368*x^48-\ 988422155012723648*x^47-1328611424340516992*x^46-2177738311926879038*x^45-\ 1596665204326268112*x^44-1105428881624370722*x^43+185590541186208052*x^42+ 776623498697357200*x^41+1788809753262611180*x^40+1610816195760422306*x^39+ 1401845678707693904*x^38+577974837834111886*x^37+119759331037872964*x^36-\ 611599022007774384*x^35-690592798199163780*x^34-708917213285279822*x^33-\ 440606003342926672*x^32-276442108433622098*x^31+5593730558339024*x^30+ 88017606988549760*x^29+120986611230999088*x^28+93058401778691618*x^27+ 71699199535821380*x^26+28745246203186526*x^25+7558736132415480*x^24+ 1959786699784544*x^23+15320630140164*x^22-592380205488542*x^21-286638698161740* x^20-88033161671554*x^19-28497194371004*x^18-6453784987872*x^17+617443648412*x^ 16+684261616584*x^15+260166304016*x^14+87564069752*x^13+22059801984*x^12+ 2826671114*x^11+237136688*x^10-65794300*x^9-34020480*x^8-6653454*x^7-1109280*x^ 6-610662*x^5-66432*x^4+3114*x^3-3840*x^2-1370*x+320)/(x-1)^2/(x^8+3*x^7+6*x^6-x ^5+15*x^4-x^3+6*x^2+3*x+1)^2/(x^16-5*x^15+10*x^14-10*x^13-28*x^12+10*x^11+110*x ^10+110*x^9+88*x^8+110*x^7+110*x^6+10*x^5-28*x^4-10*x^3+10*x^2-5*x+1)^2/(x^16-5 *x^15-23*x^14-10*x^13-94*x^12-485*x^11+242*x^10+110*x^9+649*x^8+110*x^7+242*x^6 -485*x^5-94*x^4-10*x^3-23*x^2-5*x+1)^2 The asympotics is (320+119759331037872964*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^ 11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z ^2-5*_Z+1,index = 1)^36-611599022007774384*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^ 13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94 *_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^35-690592798199163780*RootOf(_Z^16-5*_Z ^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+ 242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^34-\ 708917213285279822*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+ 242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-\ 5*_Z+1,index = 1)^33-440606003342926672*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-\ 94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z ^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^32-276442108433622098*RootOf(_Z^16-5*_Z^15 -23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242* _Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^31+5593730558339024* RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^ 30+88017606988549760*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+ 242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-\ 5*_Z+1,index = 1)^29+120986611230999088*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-\ 94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z ^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^28+93058401778691618*RootOf(_Z^16-5*_Z^15-\ 23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242* _Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^27+71699199535821380* RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^ 26+28745246203186526*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+ 242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-\ 5*_Z+1,index = 1)^25+7558736132415480*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94 *_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4 -10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^24+1959786699784544*RootOf(_Z^16-5*_Z^15-23* _Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6 -485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^23+15320630140164*RootOf(_Z ^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^22-\ 592380205488542*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242* _Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z +1,index = 1)^21-286638698161740*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^ 12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10* _Z^3-23*_Z^2-5*_Z+1,index = 1)^20-88033161671554*RootOf(_Z^16-5*_Z^15-23*_Z^14-\ 10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485* _Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^19-28497194371004*RootOf(_Z^16-5 *_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^ 7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^18-6453784987872* RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^ 17+617443648412*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242* _Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z +1,index = 1)^16+684261616584*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-\ 485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^ 3-23*_Z^2-5*_Z+1,index = 1)^15+260166304016*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z ^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-\ 94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^14+87564069752*RootOf(_Z^16-5*_Z^15-\ 23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242* _Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^13+22059801984*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^12+ 2826671114*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+ 110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1, index = 1)^11+237136688*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^ 11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z ^2-5*_Z+1,index = 1)^10-65794300*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^ 12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10* _Z^3-23*_Z^2-5*_Z+1,index = 1)^9-34020480*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^ 13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94 *_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^8-6653454*RootOf(_Z^16-5*_Z^15-23*_Z^14 -10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485* _Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^7-1109280*RootOf(_Z^16-5*_Z^15-\ 23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242* _Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^6-610662*RootOf(_Z^16-5 *_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^ 7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^5-1370*RootOf(_Z^ 16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110 *_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)-66432*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^4+3114* RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^3 -3840*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110* _Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^2+286720*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10 +110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1, index = 1)^86-4407200*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11 +242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2 -5*_Z+1,index = 1)^85+12552832*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-\ 485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^ 3-23*_Z^2-5*_Z+1,index = 1)^84+51804128*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-\ 94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z ^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^83-140078160*RootOf(_Z^16-5*_Z^15-23*_Z^14 -10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485* _Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^82-223042112*RootOf(_Z^16-5*_Z^ 15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+ 242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^81+3392556960* RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^ 80-6772574688*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^ 10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1, index = 1)^79-32998308048*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485* _Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23 *_Z^2-5*_Z+1,index = 1)^78+37874334944*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-\ 94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z ^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^77+159383937616*RootOf(_Z^16-5*_Z^15-23*_Z ^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-\ 485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^76-1048771754582*RootOf(_Z^ 16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110 *_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^75+ 1215139671232*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^ 10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1, index = 1)^74+8239060471446*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485 *_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-\ 23*_Z^2-5*_Z+1,index = 1)^73-1765281505312*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^ 13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94 *_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^72-31306266572154*RootOf(_Z^16-5*_Z^15-\ 23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242* _Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^71+140453959471792* RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^ 70-109339756667154*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+ 242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-\ 5*_Z+1,index = 1)^69-756837798553936*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94* _Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-\ 10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^68-727369523814740*RootOf(_Z^16-5*_Z^15-23*_Z ^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-\ 485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^67+2864334083478544*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^66-\ 10477687896754602*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242 *_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5* _Z+1,index = 1)^65+11279194115203312*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94* _Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-\ 10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^64+15663965414461944*RootOf(_Z^16-5*_Z^15-23* _Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6 -485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^63+50243800946136208*RootOf (_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8 +110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^62+ 7585150625375352*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242* _Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z +1,index = 1)^61-1596665204326268112*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94* _Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-\ 10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^44-1105428881624370722*RootOf(_Z^16-5*_Z^15-\ 23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242* _Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^43+185590541186208052* RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^ 42+776623498697357200*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11 +242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2 -5*_Z+1,index = 1)^41+1788809753262611180*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^ 13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94 *_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^40+1610816195760422306*RootOf(_Z^16-5* _Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7 +242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^39+ 1401845678707693904*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+ 242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-\ 5*_Z+1,index = 1)^38+577974837834111886*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-\ 94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z ^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^37+83669848441900164*RootOf(_Z^16-5*_Z^15-\ 23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242* _Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^60-54080107834236800* RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^ 59-101534367824757412*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11 +242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2 -5*_Z+1,index = 1)^58-318108985457311982*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13 -94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94* _Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^57-224696925497309220*RootOf(_Z^16-5*_Z^ 15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+ 242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^56-\ 429754497077154194*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+ 242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-\ 5*_Z+1,index = 1)^55-24249322681081988*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-\ 94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z ^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^54+197334828968756032*RootOf(_Z^16-5*_Z^15 -23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242* _Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^53+845234595728857624* RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^ 52+859162871503526066*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11 +242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2 -5*_Z+1,index = 1)^51+1326621361070739180*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^ 13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94 *_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^50+653400209972170158*RootOf(_Z^16-5*_Z ^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+ 242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^49+ 184838822003090368*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+ 242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-\ 5*_Z+1,index = 1)^48-988422155012723648*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-\ 94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z ^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^47-1328611424340516992*RootOf(_Z^16-5*_Z^ 15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+ 242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^46-\ 2177738311926879038*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+ 242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-\ 5*_Z+1,index = 1)^45)/(157678991870847*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-\ 94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z ^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^36+32526043946588*RootOf(_Z^16-5*_Z^15-23* _Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6 -485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^35+132732190881257*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^34+ 766637354384*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^ 10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1, index = 1)^33+57080762813800*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-\ 485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^ 3-23*_Z^2-5*_Z+1,index = 1)^32-55335582589166*RootOf(_Z^16-5*_Z^15-23*_Z^14-10* _Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5 -94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^31+6566132913791*RootOf(_Z^16-5*_Z^ 15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+ 242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^30-42825604913740* RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^ 29+4877707095877*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242* _Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z +1,index = 1)^28-18604838700918*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12 -485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z ^3-23*_Z^2-5*_Z+1,index = 1)^27+13056067861366*RootOf(_Z^16-5*_Z^15-23*_Z^14-10 *_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^ 5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^26-4445619215072*RootOf(_Z^16-5*_Z^ 15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+ 242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^25+6363548683093* RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^ 24-1322686840200*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242* _Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z +1,index = 1)^23+2015620470699*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-\ 485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^ 3-23*_Z^2-5*_Z+1,index = 1)^22-1396968424456*RootOf(_Z^16-5*_Z^15-23*_Z^14-10* _Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5 -94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^21+346965582139*RootOf(_Z^16-5*_Z^15 -23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242* _Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^20-104006964732*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^19+ 8625810578*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+ 110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1, index = 1)^18-18560853058*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485* _Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23 *_Z^2-5*_Z+1,index = 1)^17+9872459882*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94 *_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4 -10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^16-449393040*RootOf(_Z^16-5*_Z^15-23*_Z^14-\ 10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485* _Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^15-287743360*RootOf(_Z^16-5*_Z^ 15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+ 242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^14+209576258*RootOf (_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8 +110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^13+ 21339197*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+ 110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1, index = 1)^12-16512870*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^ 11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z ^2-5*_Z+1,index = 1)^11-4633684*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12 -485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z ^3-23*_Z^2-5*_Z+1,index = 1)^10+1893430*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-\ 94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z ^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^9-547646*RootOf(_Z^16-5*_Z^15-23*_Z^14-10* _Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5 -94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^8-82214*RootOf(_Z^16-5*_Z^15-23*_Z^ 14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-\ 485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^7+41217*RootOf(_Z^16-5*_Z^15 -23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242* _Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^6-2126*RootOf(_Z^16-5* _Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7 +242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^5+31*RootOf(_Z^16-\ 5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z ^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^4+310*RootOf(_Z^ 16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110 *_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^3+25*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^2+256* RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^ 82-3936*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110 *_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^81+13561*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^ 10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1, index = 1)^80+25462*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+ 242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-\ 5*_Z+1,index = 1)^79-109505*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485 *_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-\ 23*_Z^2-5*_Z+1,index = 1)^78-127534*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94* _Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-\ 10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^77+2347169*RootOf(_Z^16-5*_Z^15-23*_Z^14-10* _Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5 -94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^76-5815238*RootOf(_Z^16-5*_Z^15-23* _Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6 -485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^75-18807998*RootOf(_Z^16-5* _Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7 +242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^74+35617142*RootOf (_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8 +110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^73+ 91505964*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+ 110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1, index = 1)^72-650076646*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^ 11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z ^2-5*_Z+1,index = 1)^71+1101528029*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z ^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10 *_Z^3-23*_Z^2-5*_Z+1,index = 1)^70+4206349634*RootOf(_Z^16-5*_Z^15-23*_Z^14-10* _Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5 -94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^69-3252221952*RootOf(_Z^16-5*_Z^15-\ 23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242* _Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^68-16166109168*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^67+ 74706708010*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10 +110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1, index = 1)^66-95325329506*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485* _Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23 *_Z^2-5*_Z+1,index = 1)^65-379550104494*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-\ 94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z ^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^64-28281416636*RootOf(_Z^16-5*_Z^15-23*_Z^ 14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-\ 485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^63+1026670289755*RootOf(_Z^ 16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110 *_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^62-\ 4805954074856*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^ 10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1, index = 1)^61+185040295648362*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-\ 485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^ 3-23*_Z^2-5*_Z+1,index = 1)^44-80911849744110*RootOf(_Z^16-5*_Z^15-23*_Z^14-10* _Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5 -94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^43+3978974715441*RootOf(_Z^16-5*_Z^ 15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+ 242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^42-281809188505416* RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^ 41-96526511147055*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242 *_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5* _Z+1,index = 1)^40-218724092705646*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z ^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10 *_Z^3-23*_Z^2-5*_Z+1,index = 1)^39+11948156139882*RootOf(_Z^16-5*_Z^15-23*_Z^14 -10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485* _Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^38-65023815933952*RootOf(_Z^16-5 *_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^ 7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^37+7864315274571* RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^ 60+3173560864120*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242* _Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z +1,index = 1)^59+19059404364277*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12 -485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z ^3-23*_Z^2-5*_Z+1,index = 1)^58+1449262627552*RootOf(_Z^16-5*_Z^15-23*_Z^14-10* _Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5 -94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^57+47307004890486*RootOf(_Z^16-5*_Z^ 15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+ 242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^56-18643388024822* RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^ 55+2751119981093*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242* _Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z +1,index = 1)^54-78811374668620*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12 -485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z ^3-23*_Z^2-5*_Z+1,index = 1)^53-28497486890785*RootOf(_Z^16-5*_Z^15-23*_Z^14-10 *_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^ 5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^52-162678083457582*RootOf(_Z^16-5* _Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7 +242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^51-19179505880920* RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^ 50-66859176249520*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242 *_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5* _Z+1,index = 1)^49+123125419626953*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z ^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10 *_Z^3-23*_Z^2-5*_Z+1,index = 1)^48+47544998356508*RootOf(_Z^16-5*_Z^15-23*_Z^14 -10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485* _Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^47+287618211709791*RootOf(_Z^16-\ 5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110*_Z ^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^46+ 91051365643392*RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z ^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1 ,index = 1)^45)*(1/RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+ 242*_Z^10+110*_Z^9+649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-\ 5*_Z+1,index = 1))^n*(1+n) and in decimals 66.2255687894783828512695965406398914633981056592340874687572609744185698894\ 093700542058700970753817648899087693045085739112095720640039854131658951\ 571557440931015033354631466747861586730893761429280538591926917220910964\ 217724568633834016384764301556658156405373510993035251149371406374651866\ 689681317 8.2162711147018080784197270517005864370282025075930083403333260\ 117064480028303210164396856662174399195946389796610422925862284083314839\ 778012159810515685972390535991856544254562496688680657230705296469120288\ 620364097069099701982492789686403867857901482172252948165026090017551165\ n 6134298623976970864339 (1. + n) The BZ constant is (-679706465817808500121535750004371675876627498418571087880556499536000*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^30-\ 4372240545504121962422617018242739252384096288168555642134177934020560*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^29-\ 11688171756051901949784366984304458262771136935638379665471442732518160*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^28-\ 39647405839933715668058222748187440295400113996044024850666339394196240*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^27-\ 162223513796612777974420675083951609877561067993994114269671990031346560*RootOf (_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8 +110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^26-\ 281536693169838739964431406098732583778525366632616614075296926932334960*RootOf (_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8 +110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^25-\ 307698536009527805382033640795933121299695442843043958313060551722173840*RootOf (_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8 +110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^24-\ 997285569167374723892614256941515586519017351075318870552897183518986640*RootOf (_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8 +110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^23-\ 783226547969740633369942879523786820954770248633267421383144492086337360*RootOf (_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8 +110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^22+ 3468682315830287566341584528215016932827126131620806081414829444595730880* RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^ 21+3118612324571360846922547743612984364651350097641517462667209604105568480* RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^ 20+5262741596524696353063583079168274790600415009189733938836513512106958080* RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^ 19-2504534116094177172358259351816707008652810964256437790858477522459741840* RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^ 18-3163776822737833234267400085722634880866966353370624493344613293470160320* RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^ 17-10766460428268082730507916916727135546284022337841088253874405347032526640* RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^ 16-740332123578025500222031014898954952393875254000204592857198583812505840* RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^ 15-377592995437633774103826148222412192847654945282892140761032112170392000* RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^ 14+6375420274084023132058289364431384757474157055960276133933901428790789760* RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^ 13+2403148296972031436656451838454382346262430081102877103187049986340974400* RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^ 12+2368198641376100857217718315136627419829441984966177487328457670231079280* RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^ 11-1770323902670224624783234187972641058191125571205146579748646065788792000* RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^ 10-784435807102817627107640735654486200674677662794148083968503193936268960* RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^9 -134840105356347387547720738247227011764776591973773285719522304429751680* RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^8 -245552611409977313004194393985303535202089391347744362684512465275250880* RootOf(_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+ 649*_Z^8+110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^7 -99516246493911380064244522129143754502957834358875353120286380296584880*RootOf (_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8 +110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^6-\ 5502707106772638281853533752767240793195805658915639016296787242930480*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^5+ 98235738436997516828928608573186713989415993160420717503961056021600*RootOf(_Z^ 16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110 *_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)-\ 10068664702056489421481773066378830867184123092989741795623329691680-\ 4944860433990238884442052571382442737033198077829018045602712783410960*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^4-\ 2058548628333031480529343393728949435679383795306678748952104343680800*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^3+ 235503595508063374393863000381142815424906041507301544430548864220560*RootOf(_Z ^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^2)/( 10495719663672047409166204888922890207913440953462788676945318845838*RootOf(_Z^ 16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110 *_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^30+ 67514159968923454305755866141657624125183378186109771892984369039010*RootOf(_Z^ 16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110 *_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^29+ 180483459106613982440220379877432314488065624995585128015000234012426*RootOf(_Z ^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^28+ 612217299680059914504495461557115490691536843918251829714986851240527*RootOf(_Z ^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^27+ 2504982090362241029620281895832826224714264340067328384991487607591340*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^26+ 4347362214428265177991629713981569353625526913596273393229840836992119*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^25+ 4751341553063420651749708508607779614156071581416882698290152563789741*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^24+ 15399632465000343803982360492491271230278237035697067042823273169092582*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^23+ 12094229927482609600923209780016770510224211564135131609142064383923059*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^22-\ 53561822667874271420339689103007566786126191588252435830524743491198072*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^21-\ 48156200274760456076446488157544821173646848140620271130108429640374300*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^20-\ 81264874229964318696629270368568797484185699009238612837474698205453418*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^19+ 38673882466332804728407223091003423382543016068191276300121425048188910*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^18+ 48853610016873490674270368789717243823025476240513390823746727315991406*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^17+ 166250809877355853856284488691071989511783505352065599362932264964783664*RootOf (_Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8 +110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^16+ 11431873634748925414591880745304147015945972201212983105378484467892420*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^15+ 5830620167667540063651234281962200593236385375144771182122211744266438*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^14-\ 98446354856816043191288300126564357894053417603835125579472102547736155*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^13-\ 37108328524433674267986055555896029217928071323261937762496329712543215*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^12-\ 36568651759180278522423185345143784330549863952344268265972134872985640*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^11+ 27336540594979638401195008757110967458384500373904478460165797378589068*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^10+ 12112902759105678955156056243681405201404598871804458459242945508483507*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^9+ 2082139888814309071105898962208485595166698239412047328835385844148594*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^8+ 3791712307499479805663535525184474014084483233151535702390161312427554*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^7+ 1536684845102298413879491171392172060399147858985300341510519866430854*RootOf( _Z^16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+ 110*_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^6+ 84970313048081812610518399566627805608141848010261324901870253326416*RootOf(_Z^ 16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110 *_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^5+ 155475764040365599142856441031389630380950370714369021504978229156-\ 1516911819147491369875634171983103519026538814450682218776397687573*RootOf(_Z^ 16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110 *_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)+ 76356297164799165715789664952237637622948611157562347105487472643727*RootOf(_Z^ 16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110 *_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^4+ 31787176380919241035629380644550343159016817942907598860591498136008*RootOf(_Z^ 16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110 *_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^3-\ 3636539951336953991679921037752072508660853664935999398873542083214*RootOf(_Z^ 16-5*_Z^15-23*_Z^14-10*_Z^13-94*_Z^12-485*_Z^11+242*_Z^10+110*_Z^9+649*_Z^8+110 *_Z^7+242*_Z^6-485*_Z^5-94*_Z^4-10*_Z^3-23*_Z^2-5*_Z+1,index = 1)^2) and in decimals .340179868924112836772060183916870487107478540491420808722455473554087114986963\ 7106305885610306541613274353498978178840660433379254041238701241735752591276975\ 0644465452717178780407367931860440780427263450567398621830465070799934794136310\ 1462588363918981508452229798728810125730471076495085301799232086 -------------------------------- This took, 3261.664, seconds. [[1/(x^2-3*x+1), 2*(x^2-x+1)*(x^3-x^2-2*x+1)/(x^2-3*x+1)^2], [-(4*x^2+x+3)/(x-1 )/(x^4-4*x^3-x^2-4*x+1), (32*x^12-272*x^11+452*x^10+376*x^9+816*x^8+12*x^7-8*x^ 6-232*x^5+16*x^4-40*x^3+18*x^2-24*x+6)/(x-1)^2/(x^4-4*x^3-x^2-4*x+1)^2], [(36*x ^10+20*x^9-76*x^8+103*x^7-49*x^6-608*x^5-112*x^4+112*x^3+5*x^2+13*x+16)/(x^6-3* x^5+6*x^4-10*x^3+6*x^2-3*x+1)/(x^8-4*x^7-17*x^6+8*x^5+49*x^4+8*x^3-17*x^2-4*x+1 ), (2016*x^31-26424*x^30+76784*x^29+177840*x^28-805992*x^27+336572*x^26+1406432 *x^25-6628092*x^24+9345048*x^23+17151224*x^22-35171192*x^21+20561596*x^20+ 9552176*x^19-140184504*x^18+76273480*x^17+138809200*x^16-6890160*x^15-26763408* x^14-13830680*x^13-8491192*x^12+1139888*x^11+2000920*x^10+599424*x^9+149240*x^8 -31696*x^7-9420*x^6-3120*x^5-2644*x^4+976*x^3-144*x^2-184*x+36)/(x^6-3*x^5+6*x^ 4-10*x^3+6*x^2-3*x+1)^2/(x^8-4*x^7-17*x^6+8*x^5+49*x^4+8*x^3-17*x^2-4*x+1)^2], [-(576*x^36+1072*x^35+880*x^34+9397*x^33+37352*x^32-38820*x^31-162696*x^30-\ 409945*x^29-940188*x^28-6830079*x^27-10208568*x^26-12657852*x^25-11172468*x^24-\ 10598248*x^23+2897948*x^22+13501001*x^21+22499688*x^20+26110019*x^19+28239293*x ^18+18386448*x^17+10158616*x^16+2700085*x^15-4176485*x^14-10893240*x^13-8747319 *x^12-7446180*x^11-6025584*x^10-4322484*x^9-802676*x^8-189560*x^7-61343*x^6+ 7796*x^5+19551*x^4+5928*x^3+1012*x^2+296*x+125)/(x-1)/(x^8+3*x^7+6*x^6-x^5+15*x ^4-x^3+6*x^2+3*x+1)/(x^16-5*x^15+10*x^14-10*x^13-28*x^12+10*x^11+110*x^10+110*x ^9+88*x^8+110*x^7+110*x^6+10*x^5-28*x^4-10*x^3+10*x^2-5*x+1)/(x^16-5*x^15-23*x^ 14-10*x^13-94*x^12-485*x^11+242*x^10+110*x^9+649*x^8+110*x^7+242*x^6-485*x^5-94 *x^4-10*x^3-23*x^2-5*x+1), (286720*x^86-4407200*x^85+12552832*x^84+51804128*x^ 83-140078160*x^82-223042112*x^81+3392556960*x^80-6772574688*x^79-32998308048*x^ 78+37874334944*x^77+159383937616*x^76-1048771754582*x^75+1215139671232*x^74+ 8239060471446*x^73-1765281505312*x^72-31306266572154*x^71+140453959471792*x^70-\ 109339756667154*x^69-756837798553936*x^68-727369523814740*x^67+2864334083478544 *x^66-10477687896754602*x^65+11279194115203312*x^64+15663965414461944*x^63+ 50243800946136208*x^62+7585150625375352*x^61+83669848441900164*x^60-\ 54080107834236800*x^59-101534367824757412*x^58-318108985457311982*x^57-\ 224696925497309220*x^56-429754497077154194*x^55-24249322681081988*x^54+ 197334828968756032*x^53+845234595728857624*x^52+859162871503526066*x^51+ 1326621361070739180*x^50+653400209972170158*x^49+184838822003090368*x^48-\ 988422155012723648*x^47-1328611424340516992*x^46-2177738311926879038*x^45-\ 1596665204326268112*x^44-1105428881624370722*x^43+185590541186208052*x^42+ 776623498697357200*x^41+1788809753262611180*x^40+1610816195760422306*x^39+ 1401845678707693904*x^38+577974837834111886*x^37+119759331037872964*x^36-\ 611599022007774384*x^35-690592798199163780*x^34-708917213285279822*x^33-\ 440606003342926672*x^32-276442108433622098*x^31+5593730558339024*x^30+ 88017606988549760*x^29+120986611230999088*x^28+93058401778691618*x^27+ 71699199535821380*x^26+28745246203186526*x^25+7558736132415480*x^24+ 1959786699784544*x^23+15320630140164*x^22-592380205488542*x^21-286638698161740* x^20-88033161671554*x^19-28497194371004*x^18-6453784987872*x^17+617443648412*x^ 16+684261616584*x^15+260166304016*x^14+87564069752*x^13+22059801984*x^12+ 2826671114*x^11+237136688*x^10-65794300*x^9-34020480*x^8-6653454*x^7-1109280*x^ 6-610662*x^5-66432*x^4+3114*x^3-3840*x^2-1370*x+320)/(x-1)^2/(x^8+3*x^7+6*x^6-x ^5+15*x^4-x^3+6*x^2+3*x+1)^2/(x^16-5*x^15+10*x^14-10*x^13-28*x^12+10*x^11+110*x ^10+110*x^9+88*x^8+110*x^7+110*x^6+10*x^5-28*x^4-10*x^3+10*x^2-5*x+1)^2/(x^16-5 *x^15-23*x^14-10*x^13-94*x^12-485*x^11+242*x^10+110*x^9+649*x^8+110*x^7+242*x^6 -485*x^5-94*x^4-10*x^3-23*x^2-5*x+1)^2]]