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%I A152192 #33 Oct 17 2021 13:28:54
%S A152192 1,1,1,2,1,5,4,13,9,34,25,89,64,233,169,610,441,1597,1156,4181,3025,
%T A152192 10946,7921,28657,20736,75025,54289,196418,142129,514229,372100,
%U A152192 1346269,974169,3524578,2550409,9227465,6677056,24157817,17480761,63245986,45765225
%N A152192 a(n) = Product_{k=1..floor((n-1)/2)} (1 + 4*cos(2*Pi*k/n)^2).
%H A152192 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,2,0,-1).
%F A152192 Lim_{n->infinity} sqrt(a(n+2)/a(n)) = (sqrt(5) + 1)/2.
%F A152192 G.f.: (1+x^6-x^5-3*x^4-x^2+x)/((x^2+1)*(x^2+x-1)*(x^2-x-1)). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 26 2009
%F A152192 For n > 0, a(n) = Fibonacci(n) for n odd, and Fibonacci(n/2)^2 for n even. - _Greg Dresden_, Oct 16 2021
%t A152192 a[n_] := Product[(1 + 4*Cos[2*Pi*k/n]^2), {k, 1, Floor[(n - 1)/2]}]; a = Table[N[a[n]], {n, 0, 30}]
%t A152192 Join[{1}, Table[If[EvenQ[n], Fibonacci[(n)/2]^2, Fibonacci[n]], {n, 1, 30}]] (* _Greg Dresden_, Oct 16 2021 *)
%o A152192 (PARI) a(n) = round(prod(k=1, floor((n-1)/2), (1+4*cos(2*Pi*k/n)^2))) \\ _Colin Barker_, Apr 11 2014
%Y A152192 Cf. A152189, A152191.
%K A152192 nonn,easy
%O A152192 0,4
%A A152192 _Roger L. Bagula_ and _Gary W. Adamson_, Nov 28 2008
%E A152192 More terms and edited by _Colin Barker_, _Michel Marcus_, and _Joerg Arndt_, Apr 11 2014

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