cp's OEIS Frontend

A231485 Number of perfect matchings in the graph C_5 X C_{2n}.

%I A231485 #25 Jul 17 2025 19:08:28
%S A231485 722,9922,155682,2540032,41934482,694861522,11527389122,191304901282,
%T A231485 3175220160032,52703408458882,874800747092322,14520494659638322,
%U A231485 241020661471736882,4000620276282860032,66404949893677073282,1102233473331064193122,18295603728585969257522
%N A231485 Number of perfect matchings in the graph C_5 X C_{2n}.
%H A231485 Colin Barker, <a href="/A231485/b231485.txt">Table of n, a(n) for n = 2..819</a>
%H A231485 P. W. Kasteleyn, <a href="http://dx.doi.org/10.1016/0031-8914(61)90063-5">The Statistics of Dimers on a Lattice</a>, Physica, 27 (1961), 1209-1225.
%H A231485 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (29,-261,1029,-2001,2001,-1029,261,-29,1).
%F A231485 G.f.: 2*x^2*(361-5508*x+28193*x^2-64021*x^3+70770*x^4-38841*x^5+10278*x^6-1173*x^7+41*x^8)/((1-x)*(1-9*x+21*x^2-9*x^3+x^4)*(1-19*x+41*x^2-19*x^3+x^4)).
%F A231485 From _Seiichi Manyama_, Feb 14 2021: (Start)
%F A231485 a(n) = sqrt( Product_{j=1..n} Product_{k=1..5} (4*sin((2*j-1)*Pi/(2*n))^2 + 4*sin((2*k-1)*Pi/5)^2) ).
%F A231485 a(n) = 28*a(n-1) - 233*a(n-2) + 796*a(n-3) - 1205*a(n-4) + 796*a(n-5) - 233*a(n-6) + 28*a(n-7) - a(n-8) + 200. (End)
%t A231485 CoefficientList[Series[2*(361 - 5508*x + 28193*x^2 - 64021*x^3 + 70770*x^4 - 38841*x^5 + 10278*x^6 - 1173*x^7 + 41*x^8)/((1 - x)*(1 - 9*x + 21*x^2 - 9*x^3 + x^4)*(1 - 19*x + 41*x^2 - 19*x^3 + x^4)), {x, 0, 20}], x] (* _Wesley Ivan Hurt_, Jul 17 2025 *)
%o A231485 (PARI) Vec(2*x^2*(361-5508*x+28193*x^2-64021*x^3+70770*x^4-38841*x^5+10278*x^6-1173*x^7+41*x^8)/((1-x)*(1-9*x+21*x^2-9*x^3+x^4)*(1-19*x+41*x^2-19*x^3+x^4)) + O(x^100)) \\ _Colin Barker_, Dec 13 2014
%o A231485 (PARI) default(realprecision, 120);
%o A231485 a(n) = round(sqrt(prod(j=1, n, prod(k=1, 5, 4*sin((2*j-1)*Pi/(2*n))^2+4*sin((2*k-1)*Pi/5)^2)))); \\ _Seiichi Manyama_, Feb 14 2021
%Y A231485 Cf. A220864, A231087.
%K A231485 nonn,easy
%O A231485 2,1
%A A231485 _Sergey Perepechko_, Nov 09 2013