A136671 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.

0, 1, 2, 4, 8, 17, 37, 81, 177, 388, 850, 1864, 4088, 8966, 19664, 43128, 94591, 207464, 455026, 997999, 2188891

Offset

1,3

Comments

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}

Links

Table of n, a(n) for n=1..21.

Formula

a(0)=0;a(1)=1;a(2)=Floor[Exp[Pi/4]]; a(n)=Floor[a(n-1)*Exp[Pi/4]]

Mathematica

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}]

Crossrefs

Sequence in context: A106462 A129987 A132275 * A274114 A024557 A199409

Adjacent sequences: A136668 A136669 A136670 * A136672 A136673 A136674

Keyword

nonn,uned

Author

Roger L. Bagula, Apr 04 2008

Status

approved