A115273 a(n) = floor(n/3)*(n mod 3).

0, 0, 0, 0, 1, 2, 0, 2, 4, 0, 3, 6, 0, 4, 8, 0, 5, 10, 0, 6, 12, 0, 7, 14, 0, 8, 16, 0, 9, 18, 0, 10, 20, 0, 11, 22, 0, 12, 24, 0, 13, 26, 0, 14, 28, 0, 15, 30, 0, 16, 32, 0, 17, 34, 0, 18, 36, 0, 19, 38, 0, 20, 40, 0, 21, 42, 0, 22, 44, 0, 23, 46, 0, 24, 48, 0, 25, 50, 0, 26, 52, 0, 27, 54, 0, 28, 56

Offset: 0

Author

Zak Seidov, Jan 18 2006

Keywords

• nonn
• easy

Comments

Three arithmetic progressions interlaced: a(1)=1,2,0 and d=a(n+1)-a(n)=1,2,0. Cf. A115274(n) = n+a(n), n=1,2,3,...

Crossrefs

Cf. A115274.

Cf. A142150 (the base 2 analog), A257844, ..., A257850.

Programs

Magma

[Floor(n/3)*(n mod 3): n in [0..100]]; // Vincenzo Librandi, May 11 2015

Mathematica

Table[Floor[n/3]*Mod[n, 3], {n, 0, 86}] (* Extended to offset 0 by M. F. Hasler, May 11 2015 *)

PARI

a(n, b=3)=(n=divrem(n, b))[1]*n[2] \\ M. F. Hasler, May 10 2015

Python

from math import prod
def A115273(n): return prod(divmod(n,3)) # Chai Wah Wu, Jan 19 2023

Formula

a(3*k+1) = k, a(3*k+2) = 2*k, a(3*k+3) = 0, k >= 1.

G.f.: x^4*(2*x+1) / ((x-1)^2*(x^2+x+1)^2). - Colin Barker, May 11 2015

Extensions

a(0)-a(3) and cross-references added by M. F. Hasler, May 11 2015