A011940 a(n) = floor(n*(n-1)*(n-2)*(n-3)/30).

0, 0, 0, 0, 0, 4, 12, 28, 56, 100, 168, 264, 396, 572, 800, 1092, 1456, 1904, 2448, 3100, 3876, 4788, 5852, 7084, 8500, 10120, 11960, 14040, 16380, 19000, 21924, 25172, 28768, 32736, 37100, 41888, 47124, 52836, 59052, 65800, 73112, 81016, 89544, 98728, 108600, 119196, 130548, 142692, 155664, 169500

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 (4,-6,4,-1,1,-4,6,-4,1).

Crossrefs

Cf. A011795, A011915.

Programs

Magma

[Floor(n*(n-1)*(n-2)*(n-3)/30): n in [0..60]]; // Vincenzo Librandi, Jun 19 2012

Mathematica

CoefficientList[Series[4*x^5*(1-x+x^2)/((1-x)^4*(1-x^5)),{x,0,60}],x] (* Vincenzo Librandi, Jun 19 2012 *)
LinearRecurrence[{4,-6,4,-1,1,-4,6,-4,1},{0,0,0,0,0,4,12,28,56},60] (* Harvey P. Dale, Nov 13 2017 *)
Floor[4*Binomial[Range[0,60], 4]/5] (* G. C. Greubel, Oct 27 2024 *)

SageMath

[4*binomial(n,4)//5 for n in range(61)] # G. C. Greubel, Oct 27 2024

Formula

a(n) = 4 * A011795(n).

From R. J. Mathar, Apr 15 2010: (Start)

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) + a(n-5) - 4*a(n-6) + 6*a(n-7) - 4*a(n-8) + a(n-9).

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