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Search: id:A152090
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| A152090 |
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A product sequence: a(n)=Product[1 + 4*Cos[k*Pi/n]^2 + 16*Cos[k*Pi/n]^4, {k, 1, (n - 1)/2}]]]. |
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+0
6
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| 1, 1, 1, 3, 7, 16, 39, 91, 217, 513, 1216, 2881, 6825, 16171, 38311, 90768, 215047, 509491, 1207089, 2859841, 6775552, 16052673, 38032081, 90105811, 213479175, 505776016, 1198287271, 2838988683, 6726147337, 15935624641, 37754768064
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OFFSET
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0,4
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COMMENT
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Limiting ratio after n=30 terms is 2.369205407038926.
With a(0)=0, this is a divisibility sequence with g.f. x(1-x^2)/(1-x-3x^2-x^3+x^4). The limiting ratio is the largest zero of 1-x-3x^2-x^3+x^4. [From T. D. Noe (noe(AT)sspectra.com), Dec 22 2008]
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FORMULA
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a(n)=Product[1 + 4*Cos[k*Pi/n]^2 + 16*Cos[k*Pi/n]^4, {k, 1, (n - 1)/2}]]]
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MATHEMATICA
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bb = Table[FullSimplify[ExpandAll[Product[1 + 4*Cos[k*Pi/n]^2 + 16*Cos[k*Pi/n]^4, {k, 1, (n - 1)/2}]]], {n, 0, 30}]
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CROSSREFS
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Sequence in context: A095263 A010912 A052967 this_sequence A014140 A103439 A147321
Adjacent sequences: A152087 A152088 A152089 this_sequence A152091 A152092 A152093
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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 23 2008
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