A028484 Number of perfect matchings in graph C_{13} X P_{2n}.

1, 521, 783511, 1380947751, 2539295042077, 4737855988840963, 8887976555024756736, 16707831453322853779391, 31432720082490305392103161, 59153025307098251197953889723, 111332882561747103126702691033059, 209551070271391563571916783497390709

Offset: 0

Author

Per H. Lundow

Keywords

• nonn

References

• 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

• Sergey Perepechko, Table of n, a(n) for n = 0..300
• A. M. Karavaev, S. N. Perepechko, Dimer problem on cylinders: recurrences and generating functions, (in Russian), Matematicheskoe Modelirovanie, 2014, V.26, No.11, pp.18-22.
• Per Hakan Lundow, Enumeration of matchings in polygraphs, 1998.
• Sergey Perepechko, Generating function for A028484

Programs

PARI

{a(n) = sqrtint(4^n*polresultant(polchebyshev(2*n, 2, x/2), polchebyshev(13, 1, I*x/2)))} \\ Seiichi Manyama, Apr 17 2020

Formula

G.f.: see links.

a(n) = 2^n * sqrt(Resultant(U_{2*n}(x/2), T_{13}(i*x/2))), where T_n(x) is a Chebyshev polynomial of the first kind, U_n(x) is a Chebyshev polynomial of the second kind and i = sqrt(-1). - Seiichi Manyama, Apr 17 2020

Extensions

a(10)-a(11) from Alois P. Heinz, Dec 10 2013