A028473 Number of perfect matchings in graph P_{11} X P_{2n}.

1, 144, 51205, 21001799, 8940739824, 3852472573499, 1666961188795475, 722364079570222320, 313196612952258199679, 135818983640055277506397, 58902468764522025160456848, 25545661075321867247577262777, 11079103257893769392837296086025

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

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.

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

Vladeta Jovovic, Explicit formula, generating function and recurrence

Index entries for linear recurrences with constant coefficients, signature (780, -194881, 22377420, -1419219792, 55284715980, -1410775106597, 24574215822780, -300429297446885, 2629946465331120, -16741727755133760, 78475174345180080, -273689714665707178, 716370537293731320, -1417056251105102122, 2129255507292156360, -2437932520099475424, 2129255507292156360, -1417056251105102122, 716370537293731320, -273689714665707178, 78475174345180080, -16741727755133760, 2629946465331120, -300429297446885, 24574215822780, -1410775106597, 55284715980, -1419219792, 22377420, -194881, 780, -1).

Mathematica

T[_?OddQ, _?OddQ] = 0;
T[m_, n_] := Product[2(2+Cos[2 j Pi/(m+1)]+Cos[2 k Pi/(n+1)]), {k, 1, n/2}, {j, 1, m/2}];
a[n_] := T[2n, 11] // Round;
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, May 28 2022 *)

Prog

(PARI) {a(n) = sqrtint(polresultant(polchebyshev(2*n, 2, x/2), polchebyshev(11, 2, I*x/2)))} \\ Seiichi Manyama, Apr 13 2020

Crossrefs

Row 11 of array A099390.

Bisection of A210724 (even part).

Sequence in context: A299953 A230788 A231938 * A130118 A288909 A187169

Adjacent sequences: A028470 A028471 A028472 * A028474 A028475 A028476

Keyword

nonn

Author

Per H. Lundow

Extensions

Title corrected by Sergey Perepechko, Nov 27 2012

Status

approved