A131476 a(n) = floor(n^3/3).

0, 0, 2, 9, 21, 41, 72, 114, 170, 243, 333, 443, 576, 732, 914, 1125, 1365, 1637, 1944, 2286, 2666, 3087, 3549, 4055, 4608, 5208, 5858, 6561, 7317, 8129, 9000, 9930, 10922, 11979, 13101, 14291, 15552, 16884, 18290, 19773, 21333, 22973

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,2,-3,3,-1).

Formula

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

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

a(n) = (A057078(n) - A024001(n))/3. (End)

a(n) = (3*n^3 + 3*cos(2*Pi*n/3) + sqrt(3)*sin(2*Pi*n/3) - 3)/9. - Vladimir Reshetnikov, Oct 09 2016

a(n) = (n - 1)*n*(n + 1)/3 + floor(n/3). - Bruno Berselli, Jun 08 2017

Mathematica

Table[Quotient[n^3, 3], {n, 0, 80}] (* Vladimir Joseph Stephan Orlovsky, May 07 2011 *)

Prog

(Magma) [Floor(n^3/3): n in [0..50]]; // Vincenzo Librandi, May 08 2011
(PARI) a(n)=n^3\3 \\ Charles R Greathouse IV, May 08 2011

Crossrefs

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

Sequence in context: A368187 A005476 A316430 * A023549 A192971 A024850

Adjacent sequences: A131473 A131474 A131475 * A131477 A131478 A131479

Keyword

nonn,easy

Author

Mohammad K. Azarian, Jul 27 2007

Status

approved