A003747 Number of perfect matchings (or domino tilings) in K_5 X P_2n.

56, 4181, 313501, 23508376, 1762814681, 132187592681, 9912306636376, 743290810135501, 55736898453526181, 4179524093204328056, 313408570091871078001, 23501463232797126522001, 1762296333889692618072056, 132148723578494149228882181, 9909391972053171499548091501

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..500

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 sequences related to dominoes

Index entries for linear recurrences with constant coefficients, signature (76,-76,1).

Formula

a(n) = 76*a(n-1) - 76*a(n-2) + a(n-3), n > 3.

G.f.: -x*(x^2-75*x+56)/((x-1)*(x^2-75*x+1)). - Colin Barker, Aug 30 2012

Mathematica

CoefficientList[Series[-(x^2 - 75 x + 56)/((x - 1) (x^2 - 75 x + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 14 2013 *)

Prog

(Magma) I:=[56, 4181, 313501]; [n le 3 select I[n] else 76*Self(n-1)-76*Self(n-2)+Self(n-3): n in [1..20]]; // Vincenzo Librandi, Oct 14 2013
(PARI) Vec(-x*(x^2-75*x+56)/((x-1)*(x^2-75*x+1))+O(x^99)) \\ Charles R Greathouse IV, Jun 23 2020

Crossrefs

Sequence in context: A277770 A239816 A220108 * A049033 A271138 A271139

Adjacent sequences: A003744 A003745 A003746 * A003748 A003749 A003750

Keyword

nonn,easy

Author

Frans J. Faase

Status

approved