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%I #6 Nov 11 2013 17:13:30
%S 0,1,2,2,2,3,3,3,3,4,4,5,6,6,6,6,7,7,8,8,9,10,10,10,10,11,12,12,12,13,
%T 13,13,13,14,14,15,15,16,17,17,17,17,18,19,19,19,19,20,21,21,21,22,22,
%U 22,22,23,23,24,24,25,26,26,26,27,27,27,27,28,28,29,30,30,30,30,31,31,32,32,33,34,34
%N Partial sums of A189476.
%t t = Nest[Flatten[# /. {0->{0,1}, 1->{1,0,0}}] &, {0}, 6] (*A189476*)
%t f[n_] := t[[n]]
%t s[n_] := Sum[f[i], {i, 1, n}]; s[0] = 0;
%t Table[s[n], {n, 1, 120}] (*A189575*)
%t Accumulate[Nest[Flatten[#/.{0->{0,1},1->{1,0,0}}]&,{0},6]] (* _Harvey P. Dale_, Nov 11 2013 *)
%Y Cf. A189476, A189477, A189478.
%K nonn
%O 1,3
%A _Clark Kimberling_, Apr 23 2011
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