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%I #6 Feb 17 2021 10:51:27
%S 1,9,510,12348,351258,9806292,276018090,7769376972,218915964618,
%T 6169925169414,173923080282474,4903042542453720,138226113213225360,
%U 3896923927019062734,109864493967924549384,3097380080814655131414
%N Number of Hamiltonian cycles in C_9 X P_n.
%H Artem M. Karavaev, FlowProblem.ru web-project: <a href="https://web.archive.org/web/20161024010518/http://flowproblem.ru/cycles/hamilton-cycles">Hamilton Cycles</a> page.
%F a(1) = 1,
%F a(2) = 9,
%F a(3) = 510,
%F a(4) = 12348,
%F a(5) = 351258,
%F a(6) = 9806292,
%F a(7) = 276018090,
%F a(8) = 7769376972,
%F a(9) = 218915964618,
%F a(10) = 6169925169414,
%F a(11) = 173923080282474,
%F a(12) = 4903042542453720,
%F a(13) = 138226113213225360,
%F a(14) = 3896923927019062734,
%F a(15) = 109864493967924549384,
%F a(16) = 3097380080814655131414,
%F a(17) = 87323767337933601800838,
%F a(18) = 2461902328199084994926838,
%F a(19) = 69407973132514050824027916,
%F a(20) = 1956807009306757665486727506,
%F a(21) = 55167927811346067821770238916,
%F a(22) = 1555340096869096304430909957438,
%F a(23) = 43849442381504976630009404305836,
%F a(24) = 1236239985030143206263175998483822,
%F a(25) = 34853107030241718403722175589855382,
%F a(26) = 982607816763786715239538466269510230,
%F a(27) = 27702497854161867936556506397339968900,
%F a(28) = 781011889692865295747597816757847770816,
%F a(29) = 22018937614195816157746115864333077409670,
%F a(30) = 620776226482129138228674620305021838319798,
%F a(31) = 17501440357460810648330727168987922821448020,
%F a(32) = 493415181716445483930278856798624353063822202,
%F a(33) = 13910771718167544030594031326608909473440091914,
%F a(34) = 392184061145291034056836430996430655368129473244,
%F a(35) = 11056779662054536538877196636446210335611747389240,
%F a(36) = 311721940301200906636564410157890500349649932236784,
%F a(37) = 8788324542515357690400665578497505585329578151100314,
%F a(38) = 247767764405603594976836411571672937518209124905032248,
%F a(39) = 6985275154732826888934102651732146513978317488797520690,
%F a(40) = 196934694488562776191538724504707014005230275362083701656,
%F a(41) = 5552146913930475391896775780459411721609179830228623120556,
%F a(42) = 156530749616891711989703796217135075442161831077518444319126,
%F a(43) = 4413045251765663499265310946137401936593664772109267504474906,
%F a(44) = 124416246915040322673613754759846182187844152126259812122946616,
%F a(45) = 3507646446686897075662979908868474093975056540036976036361394350,
%F a(46) = 98890489787534994457207274283663444484620706362763287343857516354,
%F a(47) = 2788003043937198605713699332783678564131827070121580581489242363832,
%F a(48) = 78601703659302306505275756589753389215955729769060343088449899118250,
%F a(49) = 2216004688940341937766809565348458359318820508427391331962206163748948,
%F a(50) = 62475449675885188060021301740436496785039244182609196021787097992172268,
%F a(51) = 1761359906720460042297310657965406669505036434033439261695709910821397678,
%F a(52) = 49657725348070514911320431453902516867983657017740343451686271787991400924
%F and
%F a(n) = -188416a(n-51) + 835584a(n-50) + 7955456a(n-49) - 41793024a(n-48) -
%F 33238528a(n-47) + 334600192a(n-46) - 1276157184a(n-45) + 2732681344a(n-44) -
%F 2618432768a(n-43) - 5036989056a(n-42) + 11060535424a(n-41) + 27959018048a(n-40) -
%F 52440361440a(n-39) - 37908518240a(n-38) + 74330191136a(n-37) + 59186108112a(n-36) -
%F 68887152928a(n-35) - 33605932304a(n-34) + 43670159120a(n-33) + 48309187400a(n-32) +
%F 33949381128a(n-31) + 12462888472a(n-30) - 88313767808a(n-29) - 107865096688a(n-28) +
%F 20762733116a(n-27) + 153311805598a(n-26) + 152573320432a(n-25) + 38397703554a(n-24) -
%F 70575876534a(n-23) - 117036064104a(n-22) - 90546530362a(n-21) - 20062310737a(n-20) +
%F 30892900555a(n-19) + 30318783786a(n-18) + 6586175756a(n-17) - 5975151103a(n-16) -
%F 4972136691a(n-15) - 2026783228a(n-14) - 1418765189a(n-13) - 1239197497a(n-12) -
%F 576571223a(n-11) - 60031321a(n-10) + 63704924a(n-9) + 32475252a(n-8) + 6586040a(n-7) +
%F 334567a(n-6) - 152710a(n-5) - 38447a(n-4) - 2238a(n-3) + 280a(n-2) + 23a(n-1), n>52.
%K nonn
%O 1,2
%A _Artem M. Karavaev_, Sep 10 2010
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