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Search: id:A136671
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| A136671 |
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Recursion based on Exp[Pi/4]: a(n)=Floor[a(n-1)*Exp[Pi/4]] Angular domain {0,Pi/4} is the smallest self-similar piece of a sine wave. |
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1
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| 0, 1, 2, 4, 8, 17, 37, 81, 177, 388, 850, 1864, 4088, 8966, 19664, 43128, 94591, 207464, 455026, 997999, 2188891
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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The hyperbolic numbers are bigger:
f[n_] := If[n == 0, 0, Sinh[n*Pi/4]/Sinh[Pi/4]];
out2 = Table[Floor[f[n]], {n, 0, 20}]
{0, 1, 2, 6, 13, 29, 64, 140, 308, 676, 1482, 3251, 7132, 15643, 34310,
75253, 165051, 362004, 793977, 1741415, 3819411}
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FORMULA
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a(0)=0;a(1)=1;a(2)=Floor[Exp[Pi/4]]; a(n)=Floor[a(n-1)*Exp[Pi/4]]
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MATHEMATICA
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a[0] = 0; a[1] = 1; a[2] = Floor[Exp[Pi/4]]; a[n_] := a[n] = Floor[a[n - 1]*Exp[Pi/4]]; out1 = Table[a[n], {n, 0, 20}]
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CROSSREFS
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Adjacent sequences: A136668 A136669 A136670 this_sequence A136672 A136673 A136674
Sequence in context: A076892 A106462 A129987 this_sequence A024557 A025241 A004148
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 04 2008
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