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
KEYWORD
nonn,easy
AUTHOR
Sergey Perepechko, Dec 28 2014
STATUS
approved