login
Number of perfect matchings in the graph C_{11} X C_{2n}.
5

%I #43 Feb 28 2021 08:12:06

%S 1956242,643041038,294554220578,152849502772958,83804387156528018,

%T 47217865780262297342,26990513247252188990402,

%U 15550772782091243971206638,8999393061535308152171682002,5221063878050546380074377019392

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

%C This sequence satisfies a recurrence relation of order 243.

%H Seiichi Manyama, <a href="/A308761/b308761.txt">Table of n, a(n) for n = 2..361</a>

%H S. N. Perepechko, <a href="http://www.jip.ru/2016/333-361-2016.pdf">The number of perfect matchings on C_m X C_n graphs</a>, (in Russian), Information Processes, 2016, V. 16, No. 4, pp. 333-361.

%H S. N. Perepechko, <a href="https://doi.org/10.1134/S0361768819020075">Counting Near-Perfect Matchings on C_m × C_n Tori of Odd Order in the Maple System</a>, Programming and Computer Software, 45(2019), 65-72.

%H Sergey Perepechko, <a href="/A308761/a308761.pdf">Generating function</a> in Maple notation.

%F 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

%o (PARI) default(realprecision, 120);

%o 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

%Y Column k=11 of A341533.

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

%K nonn

%O 2,1

%A _Sergey Perepechko_, Jul 04 2019