A011938 a(n) = floor( n*(n-1)*(n-2)*(n-3)/28 ).

0, 0, 0, 0, 0, 4, 12, 30, 60, 108, 180, 282, 424, 612, 858, 1170, 1560, 2040, 2622, 3322, 4152, 5130, 6270, 7590, 9108, 10842, 12814, 15042, 17550, 20358, 23490, 26970, 30822, 35074, 39750, 44880, 50490, 56610, 63270, 70500, 78334, 86802, 95940, 105780

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1,0,0,1,-4,6,-4,1).

Crossrefs

Cf. A011915.

Programs

Magma

[Floor(n*(n-1)*(n-2)*(n-3)/28): n in [0..50]]; // Vincenzo Librandi, May 27 2016

Mathematica

Table[Floor[n (n-1)(n-2)(n-3)/28], {n, 0, 50}] (* Vincenzo Librandi, May 27 2016 *)
LinearRecurrence[{4,-6,4,-1,0,0,1,-4,6,-4,1},{0,0,0,0,0,4,12,30,60,108,180}, 50] (* Harvey P. Dale, Aug 10 2024 *)

PARI

concat(vector(5), Vec(2*x^5*(2-2*x+3*x^2-2*x^3+2*x^4)/((1-x)^5*(1+x+x^2+x^3+x^4+x^5+x^6)) + O(x^50))) \\ Colin Barker, May 25 2016

SageMath

[6*binomial(n,4)//7 for n in range(61)] # G. C. Greubel, Oct 27 2024

Formula

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) + a(n-7) - 4*a(n-8) + 6*a(n-9) - 4*a(n-10) + a(n-11). - Chai Wah Wu, May 25 2016

G.f.: 2*x^5*(2-2*x+3*x^2-2*x^3+2*x^4) / ((1-x)^5*(1+x+x^2+x^3+x^4+x^5+x^6)). - Colin Barker, May 25 2016