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%I #13 Feb 14 2021 05:53:11
%S 36,256,2916,38416,527076,7311616,101727396,1416468496,19727326116,
%T 274760478976,3826898412516,53301739046416,742397156205156,
%U 10340257357947136,144021201787572516,2005956552488017936,27939370476391960356,389145229905568604416,5420093847412497929316
%N a(n) = sqrt( Product_{j=1..n} Product_{k=1..4} (4*sin((2*j-1)*Pi/(2*n))^2 + 4*sin((2*k-1)*Pi/4)^2) ).
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (19, -76, 76, -19, 1)
%F a(n) = 19*a(n-1) - 76*a(n-2) + 76*a(n-3) - 19*a(n-4) + a(n-5).
%F a(n) = 18*a(n-1) - 58*a(n-2) + 18*a(n-3) - a(n-4) + 144.
%F From _Vaclav Kotesovec_, Feb 14 2021: (Start)
%F G.f.: 4*(4 - 67*x + 197*x^2 - 107*x^3 + 9*x^4) / ((1 - x)*(1 - 14*x + x^2)*(1 - 4*x + x^2)).
%F a(n) = 6 + 4*(2 + sqrt(3))^n + 4*(2 - sqrt(3))^n + (7 + 4*sqrt(3))^n + (7 - 4*sqrt(3))^n. (End)
%t Table[6 + 4 (2 + Sqrt[3])^n + 4 (2 - Sqrt[3])^n + (7 + 4 Sqrt[3])^n + (7 - 4 Sqrt[3])^n, {n, 1, 20}] // FullSimplify (* _Vaclav Kotesovec_, Feb 14 2021 *)
%o (PARI) default(realprecision, 120);
%o a(n) = round(sqrt(prod(j=1, n, prod(k=1, 4, 4*sin((2*j-1)*Pi/(2*n))^2+4*sin((2*k-1)*Pi/4)^2))));
%Y Column k=4 of A341533.
%K nonn
%O 1,1
%A _Seiichi Manyama_, Feb 14 2021