A028474 Number of perfect matchings in graph P_{12} X P_{n}.

1, 1, 233, 2131, 145601, 2332097, 106912793, 2188978117, 82741005829, 1937528668711, 65743732590821, 1666961188795475, 53060477521960000, 1412218550274852671, 43242613716069407953, 1185802123987680144427, 35457442115448212075033, 990424779934371836605849

Offset

0,3

Links

Table of n, a(n) for n=0..17.

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.

Sergey Perepechko, Generation function

Mathematica

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_] := N[t[n, 12], 16] // Round; Table[a[n], {n, 1, 15}] (* Jean-François Alcover, Dec 20 2012, after A099390 *)

Prog

(PARI) {a(n) = sqrtint(polresultant(polchebyshev(12, 2, x/2), polchebyshev(n, 2, I*x/2)))} \\ Seiichi Manyama, Apr 13 2020

Crossrefs

Row 12 of array A099390.

Sequence in context: A230392 A003537 A037033 * A101218 A250464 A221812

Adjacent sequences: A028471 A028472 A028473 * A028475 A028476 A028477

Keyword

nonn

Author

Per H. Lundow

Status

approved