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%I #15 Jan 10 2018 16:02:34
%S 450,4480,51842,631750,7840800,97964230,1227006722,15382568320,
%T 192913661250,2419663276870,30350713098272,380707349218630,
%U 4775477743210050,59902315898992000,751399441414986242,9425367683335685830,118229486214797575200,1483041587095202467270,18602909221707721745282,233350323785397856885120
%N Number of perfect matchings in the P_5 X C_{2n} graph.
%H Colin Barker, <a href="/A253150/b253150.txt">Table of n, a(n) for n = 2..900</a>
%H H. Narumi, H. Hosoya, H. Murakami, <a href="http://dx.doi.org/10.1063/1.529254">Generalized expression for the numbers of perfect matching of cylindrical m x n graphs</a>, J. Math. Physics, 32 (1991), 1885-1889.
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (24,-192,703,-1320,1320,-703,192,-24,1).
%F a(n) = 2*product(17-16*cos((2*j-1)*Pi/n)+2*cos(2*(2*j-1)*Pi/n),j=1..n).
%F 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.
%F 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).
%F 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)).
%o (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
%Y Cf. A068397, A102091, A252054.
%K nonn,easy
%O 2,1
%A _Sergey Perepechko_, Dec 28 2014
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