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]}].

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, 1, 2, 4, 22, 72, 298, 1100, 4286, 1, 2, 4, 24, 80, 352, 1344, 5504, 21760, 1, 2, 4, 26, 88, 410, 1612, 6914, 28336, 118898, 1, 2, 4, 28, 96, 472, 1904, 8528, 36096, 157472

Offset

0,3

Comments

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.

Links

Table of n, a(n) for n=0..64.

Formula

t(m,n)=2^n*Product[(1 + m*Cos[k*Pi/n]^2), {k, 1, Floor[(n - 1)/2]}].

Example

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;
1, 2, 4, 22, 72, 298, 1100, 4286;
1, 2, 4, 24, 80, 352, 1344, 5504, 21760;
1, 2, 4, 26, 88, 410, 1612, 6914, 28336, 118898;
1, 2, 4, 28, 96, 472, 1904, 8528, 36096, 157472, 675904;

Mathematica

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}]

Crossrefs

Cf. A103435 (row 4), A083694 (row 5)

Sequence in context: A123937 A138882 A074634 * A035015 A212829 A210215

Adjacent sequences: A152033 A152034 A152035 * A152037 A152038 A152039

Keyword

nonn,uned,tabl

Author

Roger L. Bagula and Gary W. Adamson, Nov 20 2008

Status

approved