login
Number of Hamiltonian cycles in C_8 X P_n.
3

%I #6 Feb 17 2021 10:51:42

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

%T 456763781330,9361593883038,191870363459178,3932475321605194,

%U 80597971743535618,1651894168575456078,33856364932336405826

%N Number of Hamiltonian cycles in C_8 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) = 10,

%F a(3) = 318,

%F a(4) = 6114,

%F a(5) = 126426,

%F a(6) = 2588218,

%F a(7) = 53055038,

%F a(8) = 1087362018,

%F a(9) = 22286085818,

%F a(10) = 456763781330,

%F a(11) = 9361593883038,

%F a(12) = 191870363459178,

%F a(13) = 3932475321605194,

%F a(14) = 80597971743535618,

%F a(15) = 1651894168575456078,

%F a(16) = 33856364932336405826,

%F a(17) = 693902471632291156946,

%F a(18) = 14221864665640856614738,

%F a(19) = 291483951760814319838934,

%F a(20) = 5974103686936428822276538,

%F a(21) = 122442126390395191122751354 and

%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), n>21.

%K nonn

%O 1,2

%A _Artem M. Karavaev_, Sep 10 2010