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%I #24 Feb 14 2021 05:51:32
%S 50,224,1058,5054,24200,115934,555458,2661344,12751250,61094894,
%T 292723208,1402521134,6719882450,32196891104,154264573058,
%U 739125974174,3541365297800,16967700514814,81297137276258,389517985866464,1866292792056050,8941945974413774,42843437080012808,205275239425650254
%N Number of perfect matchings in graph C_3 x C_{2n}
%H <a href="/index/Do#domino">Index entries for sequences related to dominoes</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6, -6, 1)
%F a(n) = 2*(((sqrt(7)+sqrt(3))/2)^n + ((sqrt(7)-sqrt(3))/2)^n)^2.
%F G.f.: 2*x^2*(25-38*x+7*x^2)/((1-x)*(1-5*x+x^2)).
%F From _Seiichi Manyama_, Feb 14 2021: (Start)
%F a(n) = sqrt( Product_{j=1..n} Product_{k=1..3} (4*sin((2*j-1)*Pi/(2*n))^2 + 4*sin((2*k-1)*Pi/3)^2) ).
%F a(n) = 5*a(n-1) - a(n-2) - 12. (End)
%o (PARI) Vec(2*x^2*(25-38*x+7*x^2)/((1-x)*(1-5*x+x^2))+O(x^66)) \\ _Joerg Arndt_, Nov 03 2013
%o (PARI) default(realprecision, 120);
%o a(n) = round(sqrt(prod(j=1, n, prod(k=1, 3, 4*sin((2*j-1)*Pi/(2*n))^2+4*sin((2*k-1)*Pi/3)^2)))); \\ _Seiichi Manyama_, Feb 14 2021
%Y Cf. A220864.
%K easy,nonn
%O 2,1
%A _Sergey Perepechko_, Nov 03 2013
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