A145404 Number of perfect matchings (or domino tilings) in O_6 X P_n.

8, 137, 2016, 30521, 459544, 6926545, 104379840, 1573019185, 23705440040, 357242140889, 5383654944672, 81131924020457, 1222661758446136, 18425567948435617, 277674141464763264, 4184561857758579553, 63061536262455564872, 950340200711850811433

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

Table of n, a(n) for n=1..18.

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 (12,47,-8,-47,12,1).

Formula

For n>6, a(n) = 12*a(n-1) + 47*a(n-2) - 8*a(n-3) - 47*a(n-4) + 12*a(n-5) + a(n-6).

G.f.: -x*(x^5 +12*x^4 -46*x^3 -4*x^2 +41*x +8)/(x^6 +12*x^5 -47*x^4 -8*x^3 +47*x^2 +12*x -1). [Colin Barker, Aug 23 2012]

Mathematica

CoefficientList[Series[-(x^5 + 12*x^4 - 46*x^3 - 4*x^2 + 41*x + 8)/(x^6 + 12*x^5 - 47*x^4 - 8*x^3 + 47*x^2 + 12*x - 1), {x, 0, 20}], x] (* Wesley Ivan Hurt, Sep 03 2022 *)
LinearRecurrence[{12, 47, -8, -47, 12, 1}, {8, 137, 2016, 30521, 459544, 6926545}, 20] (* Harvey P. Dale, Apr 21 2023 *)

Crossrefs

Sequence in context: A024283 A134053 A136472 * A101388 A281684 A050789

Adjacent sequences: A145401 A145402 A145403 * A145405 A145406 A145407

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 03 2009

Extensions

More terms from Max Alekseyev, Jun 24 2011

Status

approved