A253150 Number of perfect matchings in the P_5 X C_{2n} graph.

450, 4480, 51842, 631750, 7840800, 97964230, 1227006722, 15382568320, 192913661250, 2419663276870, 30350713098272, 380707349218630, 4775477743210050, 59902315898992000, 751399441414986242, 9425367683335685830, 118229486214797575200, 1483041587095202467270, 18602909221707721745282, 233350323785397856885120

Offset

2,1

Links

Colin Barker, Table of n, a(n) for n = 2..900

H. Narumi, H. Hosoya, H. Murakami, Generalized expression for the numbers of perfect matching of cylindrical m x n graphs, J. Math. Physics, 32 (1991), 1885-1889.

Index entries for linear recurrences with constant coefficients, signature (24,-192,703,-1320,1320,-703,192,-24,1).

Formula

a(n) = 2*product(17-16*cos((2*j-1)*Pi/n)+2*cos(2*(2*j-1)*Pi/n),j=1..n).

a(n) = 2*(((sqrt(7)+sqrt(3))/2)^n+((sqrt(7)-sqrt(3))/2)^n)^2*(((sqrt(5)+1)/2)^n+((sqrt(5)-1)/2)^n)^2.

a(n) = 24*a(n-1)-192*a(n-2)+703*a(n-3)-1320*a(n-4)+ 1320*a(n-5)-703*a(n-6)+192*a(n-7)-24*a(n-8)+a(n-9).

G.f.: 2*x^2*(225 -3160*x +15361*x^2 -34324*x^3 +38512*x^4 -22148*x^5 +6371*x^6 -824*x^7 +35*x^8)/ ((1 -x)*(1 -5*x +x^2)*(1 -3*x +x^2)*(1 -15*x +32*x^2 -15*x^3 +x^4)).

Prog

(PARI) Vec(2*x^2*(225 -3160*x +15361*x^2 -34324*x^3 +38512*x^4 -22148*x^5 +6371*x^6 -824*x^7 +35*x^8)/ ((1 -x)*(1 -5*x +x^2)*(1 -3*x +x^2)*(1 -15*x +32*x^2 -15*x^3 +x^4)) + O(x^30)) \\ Colin Barker, May 11 2017

Crossrefs

Cf. A068397, A102091, A252054.

Sequence in context: A253743 A253369 A253376 * A204224 A235438 A204719

Adjacent sequences: A253147 A253148 A253149 * A253151 A253152 A253153

Keyword

nonn,easy

Author

Sergey Perepechko, Dec 28 2014

Status

approved