OFFSET
2,1
LINKS
Colin Barker, Table of n, a(n) for n = 2..819
P. W. Kasteleyn, The Statistics of Dimers on a Lattice, Physica, 27 (1961), 1209-1225.
Index entries for linear recurrences with constant coefficients, signature (29,-261,1029,-2001,2001,-1029,261,-29,1).
FORMULA
G.f.: 2*x^2*(361-5508*x+28193*x^2-64021*x^3+70770*x^4-38841*x^5+10278*x^6-1173*x^7+41*x^8)/((1-x)*(1-9*x+21*x^2-9*x^3+x^4)*(1-19*x+41*x^2-19*x^3+x^4)).
From Seiichi Manyama, Feb 14 2021: (Start)
a(n) = sqrt( Product_{j=1..n} Product_{k=1..5} (4*sin((2*j-1)*Pi/(2*n))^2 + 4*sin((2*k-1)*Pi/5)^2) ).
a(n) = 28*a(n-1) - 233*a(n-2) + 796*a(n-3) - 1205*a(n-4) + 796*a(n-5) - 233*a(n-6) + 28*a(n-7) - a(n-8) + 200. (End)
PROG
(PARI) Vec(2*x^2*(361-5508*x+28193*x^2-64021*x^3+70770*x^4-38841*x^5+10278*x^6-1173*x^7+41*x^8)/((1-x)*(1-9*x+21*x^2-9*x^3+x^4)*(1-19*x+41*x^2-19*x^3+x^4)) + O(x^100)) \\ Colin Barker, Dec 13 2014
(PARI) default(realprecision, 120);
a(n) = round(sqrt(prod(j=1, n, prod(k=1, 5, 4*sin((2*j-1)*Pi/(2*n))^2+4*sin((2*k-1)*Pi/5)^2)))); \\ Seiichi Manyama, Feb 14 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Sergey Perepechko, Nov 09 2013
STATUS
approved