OFFSET
2,1
COMMENTS
For odd values of m the order of recurrence relation for the number of perfect matchings in C_{m} X C_{2n} graph does not exceed 3^floor(m/2).
LINKS
Seiichi Manyama, Table of n, a(n) for n = 2..443
S. N. Perepechko, The number of perfect matchings on C_m X C_n graphs, (in Russian), Information Processes, 2016, V.16, No.4, pp.333-361.
Sergey Perepechko, Generating function, in Maple notation.
FORMULA
a(n) = sqrt( Product_{j=1..n} Product_{k=1..9} (4*sin((2*j-1)*Pi/(2*n))^2 + 4*sin((2*k-1)*Pi/9)^2) ). - Seiichi Manyama, Feb 14 2021
PROG
(PARI) default(realprecision, 120);
a(n) = round(sqrt(prod(j=1, n, prod(k=1, 9, 4*sin((2*j-1)*Pi/(2*n))^2+4*sin((2*k-1)*Pi/9)^2)))); \\ Seiichi Manyama, Feb 14 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Sergey Perepechko, Jan 25 2017
STATUS
approved