A028484 - OEIS

%I #22 Apr 17 2020 23:05:59

%S 1,521,783511,1380947751,2539295042077,4737855988840963,

%T 8887976555024756736,16707831453322853779391,

%U 31432720082490305392103161,59153025307098251197953889723,111332882561747103126702691033059,209551070271391563571916783497390709

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

%D 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.

%H Sergey Perepechko, <a href="/A028484/b028484.txt">Table of n, a(n) for n = 0..300</a>

%H A. M. Karavaev, S. N. Perepechko, <a href="http://mi.mathnet.ru/eng/mm3533">Dimer problem on cylinders: recurrences and generating functions</a>, (in Russian), Matematicheskoe Modelirovanie, 2014, V.26, No.11, pp.18-22.

%H Per Hakan Lundow, <a href="http://www.theophys.kth.se/~phl/Text/1factors2.ps.gz">Enumeration of matchings in polygraphs</a>, 1998.

%H Sergey Perepechko, <a href="/A028484/a028484.pdf">Generating function for A028484</a>

%F G.f.: see links.

%F 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

%o (PARI) {a(n) = sqrtint(4^n*polresultant(polchebyshev(2*n, 2, x/2), polchebyshev(13, 1, I*x/2)))} \\ _Seiichi Manyama_, Apr 17 2020

%K nonn

%O 0,2

%A _Per H. Lundow_

%E a(10)-a(11) from _Alois P. Heinz_, Dec 10 2013