A011889 a(n) = floor(n*(n-1)*(n-2)/7).

0, 0, 0, 0, 3, 8, 17, 30, 48, 72, 102, 141, 188, 245, 312, 390, 480, 582, 699, 830, 977, 1140, 1320, 1518, 1734, 1971, 2228, 2507, 2808, 3132, 3480, 3852, 4251, 4676, 5129, 5610, 6120, 6660, 7230, 7833, 8468, 9137, 9840, 10578, 11352, 12162, 13011, 13898, 14825, 15792, 16800

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

Crossrefs

Cf. A011886.

Programs

Magma

[Floor(n*(n-1)*(n-2)/7): n in [0..50]]; // Vincenzo Librandi, Jul 07 2012

Mathematica

CoefficientList[Series[x^4*(3-x+2*x^2+x^4+x^5)/((-1+x)^4*(1+x+x^2+x^3+ x^4+x^5+x^6)),{x,0,50}],x] (* Vincenzo Librandi Jul 07 2012 *)
Floor[6*Binomial[Range[0,50], 3]/7] (* G. C. Greubel, Oct 06 2024 *)

SageMath

[6*binomial(n,3)//7 for n in range(51)] # G. C. Greubel, Oct 06 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-7) - 3*a(n-8) + 3*a(n-9) - a(n-10).

G.f.: x^4*(3-x+2*x^2+x^4+x^5) / ( (1-x)^4*(1+x+x^2+x^3+x^4+x^5+x^6) ). (End)