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a(n) = a(n-1) + a(n-2) - [a(n-2)/4] - [a(n-3)/2] - [a(n-4)/4].
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%I #9 Mar 12 2014 16:37:14

%S 1,1,2,3,5,7,10,14,18,23,28,34,40,47,53,61,68,77,85,94,103,113,123,

%T 134,146,158,171,184,198,212,227,241,257,272,289,305,322,339,357,375,

%U 394,414,434,455,476,498,520,543,565,589,612

%N a(n) = a(n-1) + a(n-2) - [a(n-2)/4] - [a(n-3)/2] - [a(n-4)/4].

%C The limiting ratio a(n+1)/a(n) at the 500th iteration is:1.0039960716583698

%F a(n)=a(n-1)+a(n-2)-Floor[a(n-2)/4]-Floor[a(n-3)/2]-Floor[a(n-4)/4]

%t f[-2] = 0; f[-1] = 0; f[0] = 1; f[1] = 1;

%t f[n_] := f[n] = f[n -

%t 1] + f[n - 2] - Floor[f[n - 2]/4] - Floor[f[n - 3]/2] - Floor[f[n - 4]/4]

%t Table[f[n], {n, 0, 50}]

%K nonn

%O 0,3

%A _Roger L. Bagula_, Nov 23 2010