A180585 Number of Hamiltonian cycles in C_9 X P_n.

1, 9, 510, 12348, 351258, 9806292, 276018090, 7769376972, 218915964618, 6169925169414, 173923080282474, 4903042542453720, 138226113213225360, 3896923927019062734, 109864493967924549384, 3097380080814655131414, 87323767337933601800838, 2461902328199084994926838

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

Artem M. Karavaev, FlowProblem.ru web-project: Hamilton Cycles page.

Index entries for linear recurrences with constant coefficients, order 51.

Formula

a(n) = -188416a(n-51) + 835584a(n-50) + 7955456a(n-49) - 41793024a(n-48) -

33238528a(n-47) + 334600192a(n-46) - 1276157184a(n-45) + 2732681344a(n-44) -

2618432768a(n-43) - 5036989056a(n-42) + 11060535424a(n-41) + 27959018048a(n-40) -

52440361440a(n-39) - 37908518240a(n-38) + 74330191136a(n-37) + 59186108112a(n-36) -

68887152928a(n-35) - 33605932304a(n-34) + 43670159120a(n-33) + 48309187400a(n-32) +

33949381128a(n-31) + 12462888472a(n-30) - 88313767808a(n-29) - 107865096688a(n-28) +

20762733116a(n-27) + 153311805598a(n-26) + 152573320432a(n-25) + 38397703554a(n-24) -

70575876534a(n-23) - 117036064104a(n-22) - 90546530362a(n-21) - 20062310737a(n-20) +

30892900555a(n-19) + 30318783786a(n-18) + 6586175756a(n-17) - 5975151103a(n-16) -

4972136691a(n-15) - 2026783228a(n-14) - 1418765189a(n-13) - 1239197497a(n-12) -

576571223a(n-11) - 60031321a(n-10) + 63704924a(n-9) + 32475252a(n-8) + 6586040a(n-7) +

334567a(n-6) - 152710a(n-5) - 38447a(n-4) - 2238a(n-3) + 280a(n-2) + 23a(n-1), n>52.

Crossrefs

Column k=9 of A359855.

Sequence in context: A277360 A332149 A112910 * A102909 A367552 A230671

Adjacent sequences: A180582 A180583 A180584 * A180586 A180587 A180588

Keyword

nonn,easy

Author

Artem M. Karavaev, Sep 10 2010

Extensions

a(17) onwards from Andrew Howroyd, Feb 18 2025

Status

approved