A011912 a(n) = floor(n*(n-1)*(n-2)/30).

0, 0, 0, 0, 0, 2, 4, 7, 11, 16, 24, 33, 44, 57, 72, 91, 112, 136, 163, 193, 228, 266, 308, 354, 404, 460, 520, 585, 655, 730, 812, 899, 992, 1091, 1196, 1309, 1428, 1554, 1687, 1827, 1976, 2132, 2296, 2468, 2648, 2838, 3036, 3243, 3459, 3684, 3920, 4165, 4420, 4685, 4960, 5247, 5544, 5852, 6171, 6501, 6844, 7198, 7564, 7942, 8332, 8736, 9152, 9581, 10023, 10478, 10948

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 (3,-3,1,0,1,-3,3,-1).

Crossrefs

Cf. A011886.

Programs

Magma

[Floor(n*(n-1)*(n-2)/30): n in [0..80]]; // Vincenzo Librandi, Jul 07 2012

Maple

seq(floor(binomial(n,3)/5), n=0..80); # Zerinvary Lajos, Jan 12 2009

Mathematica

Table[Floor[(n(n-1)(n-2))/30],{n,0,80}] (* or *) LinearRecurrence[{3,-3,1,0, 1,-3,3,-1},{0,0,0,0,0,2,4,7},81] (* Harvey P. Dale, Jun 20 2011 *)
CoefficientList[Series[x^5*(x^2-2*x+2)/((-1+x)^4*(x^4+x^3+x^2+x+1)),{x,0,80}],x] (* Vincenzo Librandi, Jul 07 2012 *)

SageMath

[binomial(n,3)//5 for n in range(81)] # G. C. Greubel, Oct 19 2024

Formula

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

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

G.f.: x^5*(2-2*x+x^2) / ( (1-x)^4*(1+x+x^2+x^3+x^4) ). (End)