This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A189638 #6 Mar 30 2012 18:57:25
%S A189638 0,0,1,1,1,2,2,3,4,4,4,5,5,5,6,6,7,8,8,8,9,9,10,11,11,12,13,13,13,14,
%T A189638 14,14,15,15,16,17,17,17,18,18,18,19,19,20,21,21,21,22,22,23,24,24,25,
%U A189638 26,26,26,27,27,27,28,28,29,30,30,30,31,31,32,33,33,34,35,35,35,36,36,37,38,38,39,40
%N A189638 Partial sums of A116178.
%C A189638 See A116178.
%F A189638 s(n)=s([(n+1)/3])+[n/3], where s(0)=0.
%t A189638 t = Nest[Flatten[# /. {0->{0,0,1}, 1->{0,1,1}}] &, {0}, 5] (*A116178*)
%t A189638 f[n_] := t[[n]]
%t A189638 Flatten[Position[t, 0]] (*A189636*)
%t A189638 Flatten[Position[t, 1]] (*A189637*)
%t A189638 s[n_] := Sum[f[i], {i, 1, n}]; s[0] = 0;
%t A189638 Table[s[n], {n, 1, 120}] (*A189638*)
%Y A189638 Cf. A116178, A189636, A189637.
%K A189638 nonn
%O A189638 1,6
%A A189638 _Clark Kimberling_, Apr 24 2011