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A152190
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a(n)=2*Product[(1 + 4*Cos[k*Pi/n]^2)*(1 + 4*Sin[k*Pi/n]^2), {k, 1, Floor[(n - 1)/2]}] - Product[(1 + 4*Sin[k*Pi/n]^2), {k, 1, Floor[(n - 1)/2]}].
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0
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1, 1, 1, 12, 15, 99, 120, 725, 861, 5092, 5995, 35223, 41328, 242265, 283881, 1662716, 1947351, 11402203, 13351528, 78166989, 91523685, 535804116, 627341331, 3672559727, 4299936480, 25172370289, 29472399505, 172534703340
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OFFSET
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0,4
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COMMENTS
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It appears that Limit[Sqrt[a[n+2]/a[n]],n->Infinity]=1+(Sqrt[5]+1)/2.
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LINKS
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MATHEMATICA
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f[n_] = 2*Product[(1 + 4*Cos[k*Pi/n]^2)*(1 + 4*Sin[k*Pi/n]^2), {k, 1, Floor[(n - 1)/2]}] - Product[(1 + 4*Sin[k*Pi/n]^2), {k, 1, Floor[(n - 1)/2]}]; Table[N[f[n]], {n, 0, 30}]; Floor[%]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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