A011897 a(n) = floor(n*(n-1)*(n-2)/15).

0, 0, 0, 0, 1, 4, 8, 14, 22, 33, 48, 66, 88, 114, 145, 182, 224, 272, 326, 387, 456, 532, 616, 708, 809, 920, 1040, 1170, 1310, 1461, 1624, 1798, 1984, 2182, 2393, 2618, 2856, 3108, 3374, 3655, 3952, 4264, 4592, 4936, 5297, 5676, 6072, 6486, 6918, 7369, 7840

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)/15): n in [0..50]]; // Vincenzo Librandi, Jul 07 2012

Mathematica

CoefficientList[Series[x^4(1+x-x^2+x^3)/((1-x)^3*(1-x^5)),{x,0,45}],x]  (* Harvey P. Dale, Feb 25 2011 *)
Floor[2*Binomial[Range[0, 50], 3]/5] (* G. C. Greubel, Oct 16 2024 *)

SageMath

[2*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^4*(1+x-x^2+x^3) / ( (1-x)^4*(1+x+x^2+x^3+x^4) ). (End)