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

0,6

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,...

Links

Table of n, a(n) for n=0..86.

Formula

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

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

Mathematica

Table[Floor[n/3]*Mod[n, 3], {n, 0, 104}] \\ Extended to offset 0 by M. F. Hasler, May 11 2015

Prog

(PARI) a(n, b=3)=(n=divrem(n, b))[1]*n[2] \\ M. F. Hasler, May 10 2015
(Magma) [Floor(n/3)*(n mod 3): n in [0..100]]; // Vincenzo Librandi, May 11 2015
(Python)
from math import prod
def A115273(n): return prod(divmod(n, 3)) # Chai Wah Wu, Jan 19 2023

Crossrefs

Cf. A115274.

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

Sequence in context: A141660 A368500 A209699 * A194759 A209697 A126440

Adjacent sequences: A115270 A115271 A115272 * A115274 A115275 A115276

Keyword

nonn,easy

Author

Zak Seidov, Jan 18 2006

Extensions

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

Status

approved