A028478 Number of perfect matchings in graph C_{7} X P_{2n}.

1, 29, 1471, 79808, 4375897, 240378643, 13209069847, 725898384359, 39891876471539, 2192269974717929, 120476898663671488, 6620847045486150863, 363850801995789860221, 19995539171949615541457, 1098861359580093467365169, 60388283471627147242052029

Offset: 0

Author

Per H. Lundow

Keywords

• nonn
• easy

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..500
• Per Hakan Lundow, Enumeration of matchings in polygraphs, 1998.

Programs

PARI

{a(n) = sqrtint(4^n*polresultant(polchebyshev(2*n, 2, x/2), polchebyshev(7, 1, I*x/2)))} \\ Seiichi Manyama, Apr 17 2020

Formula

G.f.: (x^7 -42*x^6 +364*x^5 -1001*x^4 +1001*x^3 -364*x^2 +42*x -1)/( -x^8 +71*x^7 -952*x^6 +3976*x^5 -6384*x^4 +3976*x^3 -952*x^2 +71*x -1). - Alois P. Heinz, Dec 09 2013

a(n) = 2^n * sqrt(Resultant(U_{2*n}(x/2), T_{7}(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