A003743 Number of Hamiltonian cycles in O_5 X P_n.

6, 204, 4152, 90012, 1916640, 41086080, 878480688, 18801691584, 402251873664, 8607198763968, 184162678606848, 3940493249544192, 84313290894281472, 1804026190433055744, 38600161433802577920, 825915469757893794816, 17671849531462458580992

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..750

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 (16,136,-460,432,256).

Formula

a(1) = 6,

a(2) = 204,

a(3) = 4152,

a(4) = 90012,

a(5) = 1916640,

a(6) = 41086080, and

a(n) = 16a(n-1) + 136a(n-2) - 460a(n-3) + 432a(n-4) + 256a(n-5).

G.f.: 6*x*(256*x^5 -504*x^4 +234*x^3 -12*x^2 -18*x -1)/(256*x^5 +432*x^4 -460*x^3 +136*x^2 +16*x -1). - Colin Barker, Aug 30 2012

Mathematica

CoefficientList[Series[6 (256 x^5 - 504 x^4 + 234 x^3 - 12 x^2 - 18 x - 1)/(256 x^5 + 432 x^4 - 460 x^3 + 136 x^2 + 16 x - 1), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 14 2013 *)

Prog

(Magma) I:=[6, 204, 4152, 90012, 1916640, 41086080]; [n le 6 select I[n] else 16*Self(n-1)+136*Self(n-2)-460*Self(n-3)+432*Self(n-4)+256*Self(n-5): n in [1..20]]; // Vincenzo Librandi, Oct 14 2013
(PARI) Vec(6*x*(256*x^5-504*x^4+234*x^3-12*x^2-18*x-1)/(256*x^5+432*x^4-460*x^3+136*x^2+16*x-1)+O(x^99)) \\ Charles R Greathouse IV, Jun 23 2020

Crossrefs

Sequence in context: A109058 A274481 A256799 * A115491 A082405 A183595

Adjacent sequences: A003740 A003741 A003742 * A003744 A003745 A003746

Keyword

nonn,easy

Author

Frans J. Faase

Extensions

Added recurrence from Faase's web page. - N. J. A. Sloane, Feb 03 2009

Status

approved