A011903 a(n) = floor(n*(n-1)*(n-2)/21).

0, 0, 0, 0, 1, 2, 5, 10, 16, 24, 34, 47, 62, 81, 104, 130, 160, 194, 233, 276, 325, 380, 440, 506, 578, 657, 742, 835, 936, 1044, 1160, 1284, 1417, 1558, 1709, 1870, 2040, 2220, 2410, 2611, 2822, 3045, 3280

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)/21): n in [0..50]]; // Vincenzo Librandi, Jul 07 2012

Mathematica

CoefficientList[Series[x^4*(1-x+2*x^2-x^4+x^5)/((1-x)^3*(1-x^7)), {x,0,60}], x] (* Vincenzo Librandi, Jul 07 2012 *)
LinearRecurrence[{3,-3,1,0,0,0,1,-3,3,-1},{0,0,0,0,1,2,5,10,16,24},60] (* Harvey P. Dale, May 03 2023 *)

SageMath

[2*binomial(n,3)//7 for n in range(61)] # G. C. Greubel, Oct 18 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*(1-x+2*x^2-x^4+x^5) / ( (1-x)^4*(1+x+x^2+x^3+x^4+x^5+x^6) ). (End)