A189717 Partial sums of A156595.

0, 1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 6, 6, 7, 7, 7, 8, 9, 9, 10, 11, 11, 12, 12, 12, 13, 14, 14, 15, 16, 16, 17, 17, 17, 18, 18, 18, 19, 20, 20, 21, 21, 21, 22, 23, 23, 24, 25, 25, 26, 26, 26, 27, 27, 27, 28, 29, 29, 30, 30, 30, 31, 31, 31, 32, 33, 33, 34, 34, 34, 35, 36, 36, 37, 38, 38, 39, 39, 39, 40, 40

Offset: 1

Author

Clark Kimberling, Apr 26 2011

Keywords

• nonn

Comments

See A156595.

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..10000
• Kevin Ryde, Iterations of the Terdragon Curve, see index "AltTurnsR".

Crossrefs

Cf. A156595, A189715, A189716.

Programs

Mathematica

(See A189715.)

PARI

a(n) = {if(n<=0, 0, (n+1)\3 + n\3 - a(n\3))} \\ Andrew Howroyd, Sep 10 2019

PARI

a(n) = (n - subst(Pol(digits(n,3)%2),'x,-1))/2; \\ Kevin Ryde, Jul 18 2021

Python

from sympy import integer_log
def A189717(n): return sum(((m:=n//9**i)-2)//9+(m-3)//9+(m-5)//9+(m-8)//9+4 for i in range(integer_log(n,9)[0]+1)) # Chai Wah Wu, Feb 15 2025

Formula

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