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

1,5

Comments

Almost identical to A189641.

Links

Table of n, a(n) for n=1..80.

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

Formula

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

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*)

Prog

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

Crossrefs

Cf. A080846, A026225, A026179.

Sequence in context: A196376 A156077 A189641 * A058889 A226143 A166724

Adjacent sequences: A189669 A189670 A189671 * A189673 A189674 A189675

Keyword

nonn

Author

Clark Kimberling, Apr 25 2011

Status

approved