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a(0)=a(1)=a(2)=1, a(n)=a(Floor[a(n-1)/2])+a(n-Floor[a(n-1)/2]).
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%I #8 Mar 12 2014 16:37:15

%S 1,1,1,1,2,3,4,4,5,5,6,6,6,7,7,7,8,9,9,9,10,11,12,13,13,13,14,14,15,

%T 16,17,18,18,18,18,19,19,20,21,22,22,23,24,24,24,24,24,25,25,26,27,28,

%U 28,29,29,30,30,31,31,31,31,31,32,33,33,34,35,36,36,37,37,38,38,38,39,39,40,41,41,41,41,41,42,43,44,45,45,46,47,48,48,49,49,50,50,50,51,51,51,52,53

%N a(0)=a(1)=a(2)=1, a(n)=a(Floor[a(n-1)/2])+a(n-Floor[a(n-1)/2]).

%C Based on Conway's internal recursive structure, this sequence need a minimum start sequence of three ones ( here four are used) followed by a two to get started and has two alternating modes for the limiting ratio a(n+1)/a(n).

%t a[0] = 1; a[1] = 1; a[2] = 1; a[3] = 1; a[4] = 2;

%t a[n_] := a[n] = a[Floor[a[n - 1]/2]] + a[n - Floor[a[n - 1]/2]]

%t Table[a[n], {n, 0, 100}]

%Y Cf. A004001.

%K nonn

%O 0,5

%A _Roger L. Bagula_, Nov 30 2010