A180584 Number of Hamiltonian cycles in C_8 X P_n.

1, 10, 318, 6114, 126426, 2588218, 53055038, 1087362018, 22286085818, 456763781330, 9361593883038, 191870363459178, 3932475321605194, 80597971743535618, 1651894168575456078, 33856364932336405826, 693902471632291156946, 14221864665640856614738, 291483951760814319838934

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, signature (23,-34,-345,-218,22, 2919,5041,8806,11998,5873, -1318,-4467,-11373,-3848, 584,-1018,928,-84,-72,40).

Formula

a(n) = 40a(n-20) - 72a(n-19) - 84a(n-18) + 928a(n-17) - 1018a(n-16) +

584a(n-15) - 3848a(n-14) - 11373a(n-13) - 4467a(n-12) - 1318a(n-11) +

5873a(n-10) + 11998a(n-9) + 8806a(n-8) + 5041a(n-7) + 2919a(n-6) +

22a(n-5) - 218a(n-4) - 345a(n-3) - 34a(n-2) + 23a(n-1) for n>21.

G.f.: x -2*x^2 *(5 +44*x -430*x^2 +33*x^3 +93*x^4 +1471*x^5 +4596*x^6 +6807*x^7 +8263*x^8 +2751*x^9 -2482*x^10 -5126*x^11 -4711*x^12 -2094*x^13 -1406*x^14 +450*x^15 +580*x^16 -132*x^17 +32*x^18 +40*x^19)/(-1 +23*x -34*x^2 -345*x^3 -218*x^4 +22*x^5 +2919*x^6 +5041*x^7 +8806*x^8 +11998*x^9 +5873*x^10 -1318*x^11 -4467*x^12 -11373*x^13 -3848*x^14 +584*x^15 -1018*x^16 +928*x^17 -84*x^18 -72*x^19 +40*x^20) . - R. J. Mathar, Feb 28 2025

Crossrefs

Column k=8 of A359855.

Sequence in context: A291561 A302933 A372729 * A048345 A325726 A223298

Adjacent sequences: A180581 A180582 A180583 * A180585 A180586 A180587

Keyword

nonn,easy

Author

Artem M. Karavaev, Sep 10 2010

Extensions

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

Status

approved