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#33 by Hugo Pfoertner at Sun Oct 17 13:28:54 EDT 2021
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#32 by Joerg Arndt at Sun Oct 17 09:05:47 EDT 2021
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#31 by Joerg Arndt at Sun Oct 17 06:10:20 EDT 2021
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#30 by Joerg Arndt at Sun Oct 17 06:10:10 EDT 2021
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| MATHEMATICA
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Clear[f, n, k]; fa[n_] := Product[(1 + 4*Cos[2*Pi*k/n]^2), {k, 1, Floor[(n - 1)/2]}]; a = Table[N[fa[n]], {n, 0, 30}]
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proposed
editing
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#29 by Michel Marcus at Sun Oct 17 02:37:54 EDT 2021
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#28 by Michel Marcus at Sun Oct 17 02:37:49 EDT 2021
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| COMMENTS
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Lim_{n->infinity} sqrt(a(n+2)/a(n)) = (sqrt(5) + 1)/2.
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| FORMULA
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Lim_{n->infinity} sqrt(a(n+2)/a(n)) = (sqrt(5) + 1)/2.
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proposed
editing
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#27 by Wesley Ivan Hurt at Sat Oct 16 21:26:57 EDT 2021
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#26 by Wesley Ivan Hurt at Sat Oct 16 21:25:08 EDT 2021
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| FORMULA
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For n> > 0, a(n) = Fibonacci(n) for n odd, and ( Fibonacci(n/2))^)^2 for n even. - Greg Dresden, Oct 16 2021
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| MATHEMATICA
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Join[{1}, Table[If[EvenQ[n], Fibonacci[(n)/2]^2, Fibonacci[n]], {n, 1}, , 30}]] (* _Greg Dresden_, Oct 16 2021 *)
Table[If[EvenQ[n], Fibonacci[(n)/2]^2, Fibonacci[n]], {n, 1, 30}]] (* Greg Dresden, Oct 16 2021 *)
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proposed
editing
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#25 by Greg Dresden at Sat Oct 16 17:31:08 EDT 2021
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#24 by Greg Dresden at Sat Oct 16 17:30:41 EDT 2021
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| FORMULA
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For n>0, a(n) = Fibonacci(n) for n odd, and (Fibonacci(n/2))^2 for n even. - Greg Dresden, Oct 16 2021
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| MATHEMATICA
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Join[{1},
Table[If[EvenQ[n], Fibonacci[(n)/2]^2, Fibonacci[n]], {n, 1, 30}]] (* Greg Dresden, Oct 16 2021 *)
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approved
editing
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