%I #12 Apr 24 2021 03:28:15
%S 0,1,1,1,2,3,3,4,4,4,5,5,5,6,7,7,8,9,9,10,10,10,11,12,12,13,13,13,14,
%T 14,14,15,16,16,17,17,17,18,18,18,19,20,20,21,22,22,23,23,23,24,25,25,
%U 26,27,27,28,28,28,29,30,30,31,31,31,32,32,32,33,34,34,35,36,36,37,37,37,38,39,39,40
%N Partial sums of A080846.
%C Almost identical to A189641.
%H Kevin Ryde, <a href="http://user42.tuxfamily.org/terdragon/index.html">Iterations of the Terdragon Curve</a>, see index "TurnsR", with a(n) = TurnsR(n).
%F a(n) = floor((n+1)/3) + a(floor(n/3)), where a(0)=0.
%t t = Nest[Flatten[# /. {0->{0,1,0}, 1->{0,1,1}}] &, {0}, 5] (*A080846*)
%t f[n_] := t[[n]]
%t Flatten[Position[t, 0]] (* A026225 conjectured *)
%t Flatten[Position[t, 1]] (* A026179 conjectured *)
%t s[n_] := Sum[f[i], {i, 1, n}]; s[0] = 0;
%t Table[s[n], {n, 1, 120}] (*A189672*)
%o (PARI) a(n) = (n - vecsum(digits(n,3)%2))/2; \\ _Kevin Ryde_, Apr 23 2021
%Y Cf. A080846, A026225, A026179.
%K nonn
%O 1,5
%A _Clark Kimberling_, Apr 25 2011