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A152036 Triangular product sequence based 2^n times the Fibonacci version and 4 replaced with m: t(m,n)=2^n*Product[(1 + m*Cos[k*Pi/n]^2), {k, 1, Floor[(n - 1)/2]}].

%I A152036 #4 Oct 21 2012 13:40:48
%S A152036 1,1,2,1,2,4,1,2,4,14,1,2,4,16,48,1,2,4,18,56,202,1,2,4,20,64,248,880,
%T A152036 1,2,4,22,72,298,1100,4286,1,2,4,24,80,352,1344,5504,21760,1,2,4,26,
%U A152036 88,410,1612,6914,28336,118898,1,2,4,28,96,472,1904,8528,36096,157472
%N A152036 Triangular product sequence based 2^n times the Fibonacci version and 4 replaced with m: t(m,n)=2^n*Product[(1 + m*Cos[k*Pi/n]^2), {k, 1, Floor[(n - 1)/2]}].
%C A152036 The row sums are: {1, 3, 7, 21, 71, 283, 1219, 5785, 29071, 156291, 880507,...}. A sequence of sequences with the row numbers m instead of n: and the ratio increases with each row: at (1+Sqrt[5]) for m=4.
%F A152036 t(m,n)=2^n*Product[(1 + m*Cos[k*Pi/n]^2), {k, 1, Floor[(n - 1)/2]}].
%e A152036 1;
%e A152036 1, 2;
%e A152036 1, 2, 4;
%e A152036 1, 2, 4, 14;
%e A152036 1, 2, 4, 16, 48;
%e A152036 1, 2, 4, 18, 56, 202;
%e A152036 1, 2, 4, 20, 64, 248, 880;
%e A152036 1, 2, 4, 22, 72, 298, 1100, 4286;
%e A152036 1, 2, 4, 24, 80, 352, 1344, 5504, 21760;
%e A152036 1, 2, 4, 26, 88, 410, 1612, 6914, 28336, 118898;
%e A152036 1, 2, 4, 28, 96, 472, 1904, 8528, 36096, 157472, 675904;
%t A152036 f[n_, m_] = 2^n*Product[(1 + m*Cos[k*Pi/n]^2), {k, 1, Floor[(n - 1)/2]}]; Table[Table[FullSimplify[ExpandAll[f[n, m]]], {n, 0, m}], {m, 0, 10}]
%Y A152036 Cf. A103435 (row 4), A083694 (row 5)
%K A152036 nonn,uned,tabl
%O A152036 0,3
%A A152036 _Roger L. Bagula_ and _Gary W. Adamson_, Nov 20 2008