A131477 a(n) = ceiling(n^3/3).

0, 1, 3, 9, 22, 42, 72, 115, 171, 243, 334, 444, 576, 733, 915, 1125, 1366, 1638, 1944, 2287, 2667, 3087, 3550, 4056, 4608, 5209, 5859, 6561, 7318, 8130, 9000, 9931, 10923, 11979, 13102, 14292, 15552, 16885, 18291, 19773, 21334, 22974

Offset: 0

Author

Mohammad K. Azarian, Jul 27 2007

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (3, -3, 2, -3, 3, -1).

Crossrefs

Cf. A000982, A008619, A004526, A007590, A036487.

Programs

Magma

[Ceiling(n^3/3) : n in [0..50]]; // Vincenzo Librandi, Oct 01 2011

Mathematica

Ceiling[Range[0,50]^3/3] (* Harvey P. Dale, Oct 19 2013 *)

Formula

From R. J. Mathar, Dec 19 2008: (Start)

G.f.: x*(1 + 3*x^2 + 2*x^3)/((1 - x)^4*(1 + x + x^2)).

a(n) = (A001093(n) - A049347(n))/3. (End)

a(n) = floor(n^3/3 + 2/3). - Bruno Berselli, Dec 21 2017