A011887 a(n) = floor( n*(n-1)*(n-2)/5 ).

0, 0, 0, 1, 4, 12, 24, 42, 67, 100, 144, 198, 264, 343, 436, 546, 672, 816, 979, 1162, 1368, 1596, 1848, 2125, 2428, 2760, 3120, 3510, 3931, 4384, 4872, 5394, 5952, 6547, 7180, 7854, 8568, 9324, 10123, 10966

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)/5): n in [0..50]]; // Vincenzo Librandi, Jul 07 2012

Mathematica

CoefficientList[Series[x^3*(1+x+3*x^2-x^3+2*x^4)/((1-x)^3*(1-x^5)),{x,0,50}] ,x] (* Vincenzo Librandi, Jul 07 2012 *)

SageMath

[6*binomial(n,3)//5 for n in range(51)] # G. C. Greubel, Oct 16 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^3*(1+x+3*x^2-x^3+2*x^4) / ( (1-x)^4*(1+x+x^2+x^3+x^4) ). (End)