A003741 Number of perfect matchings (or domino tilings) in O_5 X P_2n.

40, 2197, 121735, 6748096, 374079619, 20737143595, 1149566489968, 63726386332735, 3532681575875629, 195834721732832344, 10856126548559080585, 601810968956118729913, 33361479413223474759160, 1849398508920455533993789, 102521677843870104359906191, 5683304262020707489694083600

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..580

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 (65,-548,995,-548,65,-1).

Formula

If b(n) denotes the number of perfect matchings (or domino tilings) in O_5 X P_n we have:

b(1) = 0,

b(2) = 40,

b(3) = 0,

b(4) = 2197,

b(5) = 0,

b(6) = 121735,

b(7) = 0,

b(8) = 6748096,

b(9) = 0,

b(10) = 374079619,

b(11) = 0,

b(12) = 20737143595, and

b(n) = 65b(n-2) - 548b(n-4) + 995b(n-6) - 548b(n-8) + 65b(n-10) - b(n-12).

G.f.: -x*(x^5 -64*x^4 +523*x^3 -850*x^2 +403*x -40)/(x^6 -65*x^5 +548*x^4 -995*x^3 +548*x^2 -65*x +1). - Colin Barker, Aug 31 2012

Mathematica

CoefficientList[Series[-(x^5 - 64 x^4 + 523 x^3 - 850 x^2 + 403 x - 40)/(x^6 - 65 x^5 + 548 x^4 - 995 x^3 + 548 x^2 - 65 x + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 14 2013 *)

Prog

(Magma) I:=[40, 2197, 121735, 6748096, 374079619, 20737143595]; [n le 6 select I[n] else 65*Self(n-1)-548*Self(n-2)+995*Self(n-3)-548*Self(n-4)+65*Self(n-5)-Self(n-6): n in [1..20]]; // Vincenzo Librandi, Oct 14 2013
(PARI) Vec(-x*(x^5-64*x^4+523*x^3-850*x^2+403*x-40)/(x^6-65*x^5+548*x^4-995*x^3+548*x^2-65*x+1)+O(x^99)) \\ Charles R Greathouse IV, Jun 23 2020

Crossrefs

Sequence in context: A060056 A223177 A140729 * A263553 A049215 A221658

Adjacent sequences: A003738 A003739 A003740 * A003742 A003743 A003744

Keyword

nonn,easy

Author

Frans J. Faase

Extensions

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

Status

approved