A189672 Partial sums of A080846.

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

Offset: 1

Author

Clark Kimberling, Apr 25 2011

Keywords

• nonn

Comments

Almost identical to A189641.

Links

• Kevin Ryde, Iterations of the Terdragon Curve, see index "TurnsR", with a(n) = TurnsR(n).

Crossrefs

Cf. A080846, A026225, A026179.

Programs

Mathematica

t = Nest[Flatten[# /. {0->{0,1,0}, 1->{0,1,1}}] &, {0}, 5] (*A080846*)
f[n_] := t[[n]]
Flatten[Position[t, 0]] (* A026225 conjectured *)
Flatten[Position[t, 1]] (* A026179 conjectured *)
s[n_] := Sum[f[i], {i, 1, n}]; s[0] = 0;
Table[s[n], {n, 1, 120}] (*A189672*)

PARI

a(n) = (n - vecsum(digits(n,3)%2))/2; \\ Kevin Ryde, Apr 23 2021

Formula

a(n) = floor((n+1)/3) + a(floor(n/3)), where a(0)=0.