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A131476
a(n) = floor(n^3/3).
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
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
KEYWORD
nonn,easy
AUTHOR
Mohammad K. Azarian, Jul 27 2007
STATUS
approved