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A178771 a(0)=0, a(1)=1, a(2)=1, a(3)=1, thereafter a(n) = If[Mod[ n, 2] == 0, a(Floor[n/2]), a(a(Floor[(n - 1)/2])) + a(n - a(Floor[( n - 3)/2]))].

%I A178771 #6 Jan 24 2019 15:42:11
%S A178771 0,1,1,1,1,2,1,2,1,2,2,3,1,4,2,3,1,4,2,3,2,4,3,5,1,4,4,5,2,5,3,6,1,4,
%T A178771 4,5,2,5,3,6,2,4,4,5,3,5,5,5,1,4,4,5,4,5,5,7,2,5,5,7,3,3,6,4,1,8,4,5,
%U A178771 4,9,5,7,2,5,5,7,3,3,6,4,2,8,4,9,4,9,5,11,3,5,5,5,5,5,5,7,1,6,4,5,4,7,5,7,4
%N A178771 a(0)=0, a(1)=1, a(2)=1, a(3)=1, thereafter a(n) = If[Mod[ n, 2] == 0, a(Floor[n/2]), a(a(Floor[(n - 1)/2])) + a(n - a(Floor[( n - 3)/2]))].
%H A178771 G. C. Greubel, <a href="/A178771/b178771.txt">Table of n, a(n) for n = 0..5000</a>
%t A178771 a[0] = 0; a[1] = 1; a[2] = 1; a[3] := 1; a[n_]:= a[n] = If[Mod[n, 2] == 0, a[Floor[n/2]], a[a[Floor[(n-1)/2]]] + a[n -a[Floor[(n-3)/2]]]]; Table[a[n], {n, 0, 200}]
%Y A178771 Cf. A002487, A004001, A178770, A178677
%K A178771 nonn
%O A178771 0,6
%A A178771 _Roger L. Bagula_, Jun 11 2010