A028480 Number of perfect matchings in graph C_{9} X P_{2n}.

1, 76, 11989, 2091817, 372713728, 66750320449, 11970180565381, 2147314732677364, 385238046548443177, 69115057977256578649, 12399917664600455876068, 2224670061782262303745381, 399128369515444836686385361, 71607684753022827432994707712

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..400
• Per Hakan Lundow, Enumeration of matchings in polygraphs, 1998.

Programs

PARI

{a(n) = sqrtint(4^n*polresultant(polchebyshev(2*n, 2, x/2), polchebyshev(9, 1, I*x/2)))} \\ Seiichi Manyama, Apr 17 2020

Formula

G.f.: (x^15 -189*x^14+9585*x^13 -194987*x^12 +1937034*x^11 -10357902*x^10 [phone]*x^9 -53951967*x^8 [phone]*x^7 -31195513*x^6 [phone]*x^5 -1937034*x^4 +194987*x^3 -9585*x^2 +189*x -1) / ( -x^16 +265*x^15 -17736*x^14 +457655*x^13 -5699687*x^12 [phone]*x^11 -146975161*x^10 [phone]*x^9 -427427424*x^8 [phone]*x^7 -146975161*x^6 [phone]*x^5 -5699687*x^4 +457655*x^3 -17736*x^2 +265*x -1). - Alois P. Heinz, Dec 10 2013

a(n) = 2^n * sqrt(Resultant(U_{2*n}(x/2), T_{9}(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