%I #26 Apr 17 2020 23:06:40

%S 1,1364,6323504,35269184041,207171729355756,1240837214254999769,

%T 7491895591984935317759,45390122553039546330628096,

%U 275408624219475075609746445361,1672150595320335623747680596071399,10155382441518040205071335049138555724

%N Number of perfect matchings in graph C_{15} X P_{2n}.

%C For odd values of m the order of recurrence relation for the number of perfect matchings in C_{m} X P_{2n} graph does not exceed 2^floor(m/2). In general, this estimate is accurate, however the case m = 15 is an exception. This sequence obeys the recurrence relation of order 120. - _Sergey Perepechko_, Apr 28 2015

%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="/A028486/b028486.txt">Table of n, a(n) for n = 0..260</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="/A028486/a028486.pdf">Generating function for A028486</a>

%F a(n) = 2^n * sqrt(Resultant(U_{2*n}(x/2), T_{15}(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(15, 1, I*x/2)))} \\ _Seiichi Manyama_, Apr 17 2020

%Y Cf. A028485, A028484.

%K nonn

%O 0,2

%A _Per H. Lundow_

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