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Number of perfect matchings in the graph C_9 X C_{2n}.
7

%I #17 Feb 14 2021 08:31:49

%S 140450,16091936,2415542018,400448833106,69206906601800,

%T 12190695635108354,2167175327735637122,387018647188487143424,

%U 69272289588070930561250,12413316310203106546620386,2225719417041514241075539592,399192630631160441128470998546

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

%C 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).

%H Seiichi Manyama, <a href="/A281583/b281583.txt">Table of n, a(n) for n = 2..443</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 Sergey Perepechko, <a href="/A281583/a281583.pdf">Generating function</a>, in Maple notation.

%F 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

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

%o 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

%Y Column k=9 of A341533.

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

%K nonn

%O 2,1

%A _Sergey Perepechko_, Jan 25 2017