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%I #15 Jan 07 2021 05:06:17
%S 1,2,4,14,48,158,532,1778,5952,19922,66676,223166,746928,2499950,
%T 8367268,28005026,93732096,313718882,1050008932,3514352558,
%U 11762446512,39368602238,131765686708,441016322834,1476070150464,4940368363442
%N a(n) = 2^n*Product_{k=1..floor((n-1)/2)} (1 + 2*cos(k*Pi/n)^2 + 4*cos(k*Pi/n)^4).
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,4,2,-1).
%F From _Colin Barker_, Jan 05 2014: (Start)
%F a(n) = 2*a(n-1) + 4*a(n-2) + 2*a(n-3) - a(n-4) for n > 5.
%F G.f.: (x^4-4*x^3-4*x^2+1) / (x^4-2*x^3-4*x^2-2*x+1). (End)
%t m = 2; l = 4; b = Table[2^n*Product[1 + m*Cos[k*Pi/n]^2 + l*Cos[k*Pi/n]^4, {k, 1, (n - 1)/2}], {n, 0, 30}]; FullSimplify[ExpandAll[%]] Round[b]
%o (PARI) Vec((x^4-4*x^3-4*x^2+1)/(x^4-2*x^3-4*x^2-2*x+1) + O(x^100)) \\ _Colin Barker_, Jan 05 2014
%K nonn,easy
%O 0,2
%A _Roger L. Bagula_, Nov 24 2008