A003749 Number of Hamiltonian cycles in K_5 X P_n.

12, 480, 13440, 382080, 10859520, 308651520, 8772556800, 249335408640, 7086662123520, 201418564362240, 5724759747624960, 162710295705845760, 4624585396735180800, 131440914657055211520, 3735840635158368092160

Offset

1,1

References

F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..700

F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.

F. Faase, Counting Hamiltonian cycles in product graphs

F. Faase, Results from the counting program

Index entries for linear recurrences with constant coefficients, signature (28,12).

Formula

a(n) = 28a(n-1) + 12a(n-2), n>2.

G.f.: 12*x*(12*x^2-12*x-1)/(12*x^2+28*x-1). - Colin Barker, Aug 30 2012

Mathematica

CoefficientList[Series[12 (12 x^2 - 12 x - 1)/(12 x^2 + 28 x - 1), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 14 2013 *)

Prog

(Magma) I:=[12, 480, 13440]; [n le 3 select I[n] else 28*Self(n-1)+12*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Oct 14 2013
(PARI) a(n)=([0, 1; 12, 28]^(n-1)*[12; 480])[1, 1] \\ Charles R Greathouse IV, Jun 23 2020

Crossrefs

Sequence in context: A262584 A350154 A241226 * A012395 A012687 A012467

Adjacent sequences: A003746 A003747 A003748 * A003750 A003751 A003752

Keyword

nonn,easy

Author

Frans J. Faase

Status

approved