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%I #2 Mar 30 2012 17:34:25
%S 0,1,2,4,8,17,37,81,177,388,850,1864,4088,8966,19664,43128,94591,
%T 207464,455026,997999,2188891
%N 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.
%C The hyperbolic numbers are bigger:
%C f[n_] := If[n == 0, 0, Sinh[n*Pi/4]/Sinh[Pi/4]];
%C out2 = Table[Floor[f[n]], {n, 0, 20}]
%C {0, 1, 2, 6, 13, 29, 64, 140, 308, 676, 1482, 3251, 7132, 15643, 34310,
%C 75253, 165051, 362004, 793977, 1741415, 3819411}
%F a(0)=0;a(1)=1;a(2)=Floor[Exp[Pi/4]]; a(n)=Floor[a(n-1)*Exp[Pi/4]]
%t 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}]
%K nonn,uned
%O 1,3
%A _Roger L. Bagula_, Apr 04 2008