cp's OEIS Frontend

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

%I A115273 #21 Aug 10 2025 18:32:07
%S A115273 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 A115273 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 A115273 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 A115273 a(n) = floor(n/3)*(n mod 3).
%C A115273 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 A115273 a(3*k+1) = k, a(3*k+2) = 2*k, a(3*k+3) = 0, k >= 1.
%F A115273 G.f.: x^4*(2*x+1) / ((x-1)^2*(x^2+x+1)^2). - _Colin Barker_, May 11 2015
%t A115273 Table[Floor[n/3]*Mod[n, 3], {n, 0, 86}] (* Extended to offset 0 by _M. F. Hasler_, May 11 2015 *)
%o A115273 (PARI) a(n, b=3)=(n=divrem(n, b))[1]*n[2] \\ _M. F. Hasler_, May 10 2015
%o A115273 (Magma) [Floor(n/3)*(n mod 3): n in [0..100]]; // _Vincenzo Librandi_, May 11 2015
%o A115273 (Python)
%o A115273 from math import prod
%o A115273 def A115273(n): return prod(divmod(n,3)) # _Chai Wah Wu_, Jan 19 2023
%Y A115273 Cf. A115274.
%Y A115273 Cf. A142150 (the base 2 analog), A257844, ..., A257850.
%K A115273 nonn,easy
%O A115273 0,6
%A A115273 _Zak Seidov_, Jan 18 2006
%E A115273 a(0)-a(3) and cross-references added by _M. F. Hasler_, May 11 2015