A028482 Number of perfect matchings in graph C_{11} X P_{2n}.

1, 199, 97021, 53924597, 30946370401, 17931360207872, 10421993545062683, 6063482153051471479, 3528867741726076542167, 2053975467997173931810469, 1195557391003219846631664779, 695906086927354589354168761123, 405072252620898699232642344701021

Offset: 0

Author

Per H. Lundow

Keywords

• nonn

References

• 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.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200
• Alois P. Heinz, G.f. for A028482
• Per Hakan Lundow, Enumeration of matchings in polygraphs, 1998.

Programs

PARI

{a(n) = sqrtint(4^n*polresultant(polchebyshev(2*n, 2, x/2), polchebyshev(11, 1, I*x/2)))} \\ Seiichi Manyama, Apr 17 2020

Formula

G.f.: see link above.

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