A189638 Partial sums of A116178.

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, 14, 14, 15, 15, 16, 17, 17, 17, 18, 18, 18, 19, 19, 20, 21, 21, 21, 22, 22, 23, 24, 24, 25, 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

Offset: 1

Author

Clark Kimberling, Apr 24 2011

Keywords

• nonn

Comments

See A116178.

Crossrefs

Cf. A116178, A189636, A189637.

Programs

Mathematica

t = Nest[Flatten[# /. {0->{0,0,1}, 1->{0,1,1}}] &, {0}, 5] (*A116178*)
f[n_] := t[[n]]
Flatten[Position[t, 0]] (*A189636*)
Flatten[Position[t, 1]] (*A189637*)
s[n_] := Sum[f[i], {i, 1, n}]; s[0] = 0;
Table[s[n], {n, 1, 120}] (*A189638*)

Formula

s(n)=s([(n+1)/3])+[n/3], where s(0)=0.