A003748 Number of 2-factors in K_5 X P_n.

12, 814, 41278, 2169266, 113488662, 5940718514, 310952704838, 16276223002786, 851946706852182, 44593472067545554, 2334157405518854758, 122176869250651741826, 6395107433748612174582, 334739295101566253176754, 17521268695699930046150918, 917116278846033398175880546

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..590

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 (47,288,-436).

Formula

a(1) = 12,

a(2) = 814,

a(3) = 41278, and

a(n) = 47a(n-1) + 288a(n-2) - 436a(n-3).

G.f.: -2*x*(218*x^2-125*x-6)/(436*x^3-288*x^2-47*x+1). - Colin Barker, Aug 30 2012

Mathematica

CoefficientList[Series[-2 (218 x^2 - 125 x - 6)/(436 x^3 - 288 x^2 - 47 x + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 14 2013 *)
LinearRecurrence[{47, 288, -436}, {12, 814, 41278}, 20] (* Harvey P. Dale, May 05 2022 *)

Prog

(Magma) I:=[12, 814, 41278]; [n le 3 select I[n] else 47*Self(n-1)+288*Self(n-2)-436*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Oct 14 2013

Crossrefs

Sequence in context: A305935 A228182 A356186 * A280333 A350412 A207817

Adjacent sequences: A003745 A003746 A003747 * A003749 A003750 A003751

Keyword

nonn,easy

Author

Frans J. Faase

Extensions

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

Status

approved