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A152036
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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]}].
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0
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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; internal format)
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OFFSET
| 0,3
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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.
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FORMULA
| t(m,n)=2^n*Product[(1 + m*Cos[k*Pi/n]^2), {k, 1, Floor[(n - 1)/2]}].
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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}
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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}]
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CROSSREFS
| Sequence in context: A123937 A138882 A074634 * A035015 A203647 A114791
Adjacent sequences: A152033 A152034 A152035 * A152037 A152038 A152039
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KEYWORD
| nonn,uned,tabl
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Nov 20 2008
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