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Search: id:A152011
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| A152011 |
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A product form based on the Fibonacci product form: f(n)=2^n*Product[(1 + 3*Cos[k*Pi/n]^2), {k, 1, Floor[(n - 1)/2]}]. |
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1
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| 1, 2, 4, 14, 40, 122, 364, 1094, 3280, 9842, 29524, 88574, 265720, 797162, 2391484, 7174454
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Gary Adamson found this article, I experimented. Based on the paper Fibonacci identity of: f[n_] = Product[(1 + 4*Cos[k*Pi/n]^2), {k, 1, Floor[(n - 1)/2]}]. I changed the 4 to a 3 and used 2^n to get rid of the rational terms. The product comes down slow in Mathematica: I tried 30 but no luck.
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REFERENCES
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O. Ramare and N. Garnier, Fibonacci numbers and trigonometric identities: http://www.tinyurl.com/66erly
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FORMULA
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f(n)=2^n*Product[(1 + 3*Cos[k*Pi/n]^2), {k, 1, Floor[(n - 1)/2]}].
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MATHEMATICA
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f[n_] = 2^n*Product[(1 + 3*Cos[k*Pi/n]^2), {k, 1, Floor[(n - 1)/2]}]; Table[FullSimplify[ExpandAll[f[n]]], {n, 0, 15}]
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CROSSREFS
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A000045
Sequence in context: A055540 A006252 A079995 this_sequence A000912 A128750 A047152
Adjacent sequences: A152008 A152009 A152010 this_sequence A152012 A152013 A152014
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KEYWORD
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nonn
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AUTHOR
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Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Nov 19 2008
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