A028482 - OEIS

%I #14 Apr 17 2020 23:05:25

%S 1,199,97021,53924597,30946370401,17931360207872,10421993545062683,

%T 6063482153051471479,3528867741726076542167,2053975467997173931810469,

%U 1195557391003219846631664779,695906086927354589354168761123,405072252620898699232642344701021

%N Number of perfect matchings in graph C_{11} 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 Alois P. Heinz, <a href="/A028482/b028482.txt">Table of n, a(n) for n = 0..200</a>

%H Alois P. Heinz, <a href="/A028482/a028482.txt">G.f. for A028482</a>

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

%F G.f.: see link above.

%F a(n) = 2^n * sqrt(Resultant(U_{2*n}(x/2), T_{11}(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(11, 1, I*x/2)))} \\ _Seiichi Manyama_, Apr 17 2020

%K nonn

%O 0,2

%A _Per H. Lundow_