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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]}]. 0
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified July 14 10:29 EDT 2020. Contains 335721 sequences. (Running on oeis4.)