A011849 a(n) = floor(binomial(n,3)/3).

0, 0, 0, 0, 1, 3, 6, 11, 18, 28, 40, 55, 73, 95, 121, 151, 186, 226, 272, 323, 380, 443, 513, 590, 674, 766, 866, 975, 1092, 1218, 1353, 1498, 1653, 1818, 1994, 2181, 2380, 2590, 2812, 3046, 3293, 3553, 3826

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4, -6, 3, 3, -6, 3, 3, -6, 4, -1).

Crossrefs

A column of triangle A011857.

Programs

Magma

[Floor(Binomial(n,3)/3): n in [0..50]]; // Vincenzo Librandi, Jun 19 2012

Maple

seq(floor(binomial(n,3)/3), n=0..42); # Zerinvary Lajos, Jan 12 2009

Mathematica

CoefficientList[Series[x^4*(x^2-x+1)*(x^3-x^2+1)/((-1+x)^4*(x^6+x^3+1)),{x,0,50}],x] (* Vincenzo Librandi, Jun 19 2012 *)

Formula

G.f.: x^4*(1-x+x^2)*(1-x^2+x^3)/((1-x)^3*(1-x^9)). - Ralf Stephan, Mar 05 2004

From R. J. Mathar, Apr 15 2010: (Start)

a(n) = 4*a(n-1) - 6*a(n-2) + 3*a(n-3) + 3*a(n-4) - 6*a(n-5) + 3*a(n-6) + 3*a(n-7) - 6*a(n-8) + 4*a(n-9) - a(n-10).

G.f.: x^4*(x^2-x+1)*(x^3-x^2+1) / ( (-1+x)^4*(x^6+x^3+1) ). (End)

a(n) = (1/54) * ( n^3 - 3*n - 6 + [6,8,4,-12,8,4,-30,8,4](mod 9) ). - Ralf Stephan, Aug 11 2013