A308761 Number of perfect matchings in the graph C_{11} X C_{2n}.

1956242, 643041038, 294554220578, 152849502772958, 83804387156528018, 47217865780262297342, 26990513247252188990402, 15550772782091243971206638, 8999393061535308152171682002, 5221063878050546380074377019392

Offset: 2

Author

Sergey Perepechko, Jul 04 2019

Keywords

• nonn

Comments

This sequence satisfies a recurrence relation of order 243.

Links

• Seiichi Manyama, Table of n, a(n) for n = 2..361
• 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.
• S. N. Perepechko, Counting Near-Perfect Matchings on C_m × C_n Tori of Odd Order in the Maple System, Programming and Computer Software, 45(2019), 65-72.
• Sergey Perepechko, Generating function in Maple notation.

Crossrefs

Column k=11 of A341533.

Cf. A230033, A231485, A232804, A253678, A281583, A281679.

Programs

PARI

default(realprecision, 120);
a(n) = round(sqrt(prod(j=1, n, prod(k=1, 11, 4*sin((2*j-1)*Pi/(2*n))^2+4*sin((2*k-1)*Pi/11)^2)))); \\ Seiichi Manyama, Feb 14 2021

Formula

a(n) = sqrt( Product_{j=1..n} Product_{k=1..11} (4*sin((2*j-1)*Pi/(2*n))^2 + 4*sin((2*k-1)*Pi/11)^2) ). - Seiichi Manyama, Feb 14 2021