A011842 a(n) = floor(n*(n-1)*(n-2)/24).

0, 0, 0, 0, 1, 2, 5, 8, 14, 21, 30, 41, 55, 71, 91, 113, 140, 170, 204, 242, 285, 332, 385, 442, 506, 575, 650, 731, 819, 913, 1015, 1123, 1240, 1364, 1496, 1636, 1785, 1942, 2109, 2284, 2470, 2665, 2870, 3085, 3311, 3547, 3795, 4053, 4324, 4606, 4900, 5206, 5525, 5856, 6201, 6558, 6930, 7315, 7714, 8127, 8555, 8997, 9455, 9927, 10416, 10920

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..2000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,0,0,0,1,-3,3,-1).

Crossrefs

A column of triangle A011847.

Cf. A011886.

Programs

Magma

[Floor(Binomial(n,3)/4): n in [0..80]]; // G. C. Greubel, Oct 20 2024

Maple

seq(floor(binomial(n,3)/4), n=0..43); # Zerinvary Lajos, Jan 12 2009

Mathematica

Floor[Binomial[Range[0,80], 3]/4] (* G. C. Greubel, Oct 20 2024 *)

SageMath

[binomial(n,3)//4 for n in range(81)] # G. C. Greubel, Oct 20 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-8) - 3*a(n-9) + 3*a(n-10) - a(n-11).

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

a(n) = floor(binomial(n+1,4)/(n+1)). - Gary Detlefs, Nov 23 2011

Extensions

More terms added by G. C. Greubel, Oct 20 2024