A003730 Number of 2-factors in C_5 X P_n.

1, 11, 81, 666, 5431, 44466, 364061, 2981201, 24412606, 199912706, 1637069691, 13405842666, 109779463516, 898976005896, 7361648869421, 60284005131851, 493661316969811, 4042556485091321, 33104199931650186

Offset

1,2

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..1000

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 (9,-4,-22,3).

Formula

a(n) = 9a(n-1) - 4a(n-2) - 22a(n-3) + 3a(n-4), n>4.

G.f.: -x*(3*x^3-14*x^2+2*x+1)/(3*x^4-22*x^3-4*x^2+9*x-1). - Colin Barker, Aug 30 2012

Mathematica

CoefficientList[Series[-(3 x^3 - 14 x^2 + 2 x + 1)/(3 x^4 - 22 x^3 - 4 x^2 + 9 x - 1), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 13 2013 *)
LinearRecurrence[{9, -4, -22, 3}, {1, 11, 81, 666}, 30] (* Harvey P. Dale, Sep 23 2016 *)

Prog

(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; 3, -22, -4, 9]^(n-1)*[1; 11; 81; 666])[1, 1] \\ Charles R Greathouse IV, Jun 23 2020

Crossrefs

Sequence in context: A227556 A181989 A199557 * A334340 A335332 A111334

Adjacent sequences: A003727 A003728 A003729 * A003731 A003732 A003733

Keyword

nonn,easy

Author

Frans J. Faase

Status

approved