A180584 - OEIS

%I #15 Feb 28 2025 10:31:44

%S 1,10,318,6114,126426,2588218,53055038,1087362018,22286085818,

%T 456763781330,9361593883038,191870363459178,3932475321605194,

%U 80597971743535618,1651894168575456078,33856364932336405826,693902471632291156946,14221864665640856614738,291483951760814319838934

%N Number of Hamiltonian cycles in C_8 X P_n.

%H Andrew Howroyd, <a href="/A180584/b180584.txt">Table of n, a(n) for n = 1..200</a>

%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.

%H <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (23,-34,-345,-218,22, 2919,5041,8806,11998,5873, -1318,-4467,-11373,-3848, 584,-1018,928,-84,-72,40).

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

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

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

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

%F 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

%Y Column k=8 of A359855.

%K nonn,easy,changed

%O 1,2

%A _Artem M. Karavaev_, Sep 10 2010

%E a(17) onwards from _Andrew Howroyd_, Feb 18 2025