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%I #8 Mar 12 2014 16:37:06
%S 1,1,2,3,4,6,7,9,11,13,16,19,22,26,29,33,37,41,46,51,56,62,67,73,79,
%T 85,92,99,106,114,121,129,137,145,154,163,172,182,191,201,211,221,232,
%U 243,254,266,277,289,301,313,326
%N a(n) = a(n-1) + a(n-2) - [a(n-2)/2] - [a(n-4)/2].
%C The female population of Rabbits is; a(n)= f[n]-Floor[f[n]/2] Here that is the term: f[n - 2] - Floor[f[n - 2]/2] One natural child birth population limit is death by infection of the mothers. The fourth generation death of old age is the Floor[f[n - 4]/2] term. The resulting sequence approaches a stable population of rabbits at ratio one.
%C The ratio on the 300th iteration is approaching 1. Henry Bottomley did some of these half floor sequences, but not in the further generations.
%F a(n)=a(n-1)+a(n-2)-Floor[a(n-2)/2]-Floor[a(n-4)/2]
%t f[-2] = 0; f[-1] = 0; f[0] = 1; f[1] = 1;
%t f[n_] := f[n] = f[n - 1] + f[n - 2] - Floor[f[n - 2]/2] - Floor[f[n - 4]/2]
%t Table[f[n], {n, 0, 50}]
%Y Cf. A023434
%K nonn
%O 0,3
%A _Roger L. Bagula_, Nov 22 2010
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