A003729 Number of perfect matchings (or domino tilings) in graph C_{5} X P_{2n}.

11, 176, 2911, 48301, 801701, 13307111, 220880176, 3666315811, 60855946601, 1010127453401, 16766766924211, 278305942640176, 4619507031938711, 76677648402694901, 1272746577484955101, 21125893715367851311

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.

Per Hakan Lundow, "Computation of matching polynomials and the number of 1-factors in polygraphs", Research report, No 12, 1996, Department of Math., Umea University, Sweden.

Links

Table of n, a(n) for n=1..16.

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

Per Hakan Lundow, Enumeration of matchings in polygraphs, 1998.

Index entries for sequences related to dominoes

Index entries for linear recurrences with constant coefficients, signature (19, -41, 19, -1).

Formula

a(n) = 19a(n-1) - 41a(n-2) + 19a(n-3) - a(n-4), n>4.

G.f. x*(11-33*x+18*x^2-x^3)/(1-19*x+41*x^2-19*x^3+x^4) . [From R. J. Mathar, Mar 11 2010]

Mathematica

Rest[CoefficientList[Series[x (11-33x+18x^2-x^3)/(1-19x+41x^2- 19x^3+ x^4), {x, 0, 20}], x]] (* or *) LinearRecurrence[{19, -41, 19, -1}, {11, 176, 2911, 48301}, 20] (* Harvey P. Dale, Jul 16 2011 *)

Crossrefs

Sequence in context: A218330 A365034 A196664 * A230388 A027398 A305970

Adjacent sequences: A003726 A003727 A003728 * A003730 A003731 A003732

Keyword

nonn,easy

Author

Frans J. Faase

Status

approved