A115273 - OEIS

%I #18 Jan 19 2023 11:06:16

%S 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,

%T 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,

%U 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

%N a(n) = floor(n/3)*(n mod 3).

%C 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,...

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

%F G.f.: x^4*(2*x+1) / ((x-1)^2*(x^2+x+1)^2). - _Colin Barker_, May 11 2015

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

%o (PARI) a(n, b=3)=(n=divrem(n, b))[1]*n[2] \\ _M. F. Hasler_, May 10 2015

%o (Magma) [Floor(n/3)*(n mod 3): n in [0..100]]; // _Vincenzo Librandi_, May 11 2015

%o (Python)

%o from math import prod

%o def A115273(n): return prod(divmod(n,3)) # _Chai Wah Wu_, Jan 19 2023

%Y Cf. A115274.

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

%K nonn,easy

%O 0,6

%A _Zak Seidov_, Jan 18 2006

%E a(0)-a(3) and cross-references added by _M. F. Hasler_, May 11 2015