A281583 Number of perfect matchings in the graph C_9 X C_{2n}.

140450, 16091936, 2415542018, 400448833106, 69206906601800, 12190695635108354, 2167175327735637122, 387018647188487143424, 69272289588070930561250, 12413316310203106546620386, 2225719417041514241075539592, 399192630631160441128470998546

Offset: 2

Author

Sergey Perepechko, Jan 25 2017

Keywords

• nonn

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.

Crossrefs

Column k=9 of A341533.

Cf. A253678, A230033, A232804, A231485, A220864, A231087.

Programs

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

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