A011893 a(n) = floor( n*(n-1)*(n-2)/11 ).

0, 0, 0, 0, 2, 5, 10, 19, 30, 45, 65, 90, 120, 156, 198, 248, 305, 370, 445, 528, 621, 725, 840, 966, 1104, 1254, 1418, 1595, 1786, 1993, 2214, 2451, 2705, 2976, 3264, 3570, 3894, 4238, 4601, 4984, 5389, 5814, 6261, 6731, 7224, 7740, 8280, 8844, 9434, 10049, 10690

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..2000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,0,0,0,0,0,0,1,-3,3,-1).

Crossrefs

Cf. A011886.

Programs

Magma

[Floor(6*Binomial(n,3)/11): n in [0..50]]; // G. C. Greubel, Oct 06 2024

Mathematica

Table[Floor[n(n-1)(n-2)/11],{n,0,40}] (* or *)
LinearRecurrence[{3,-3,1,0,0,0,0,0,0,0,1,-3,3,-1}, {0,0,0,0,2,5,10,19,30,45, 65,90,120,156}, 50] (* Harvey P. Dale, Nov 23 2018 *)

SageMath

[6*binomial(n,3)//11 for n in range(51)] # G. C. Greubel, Oct 06 2024

Formula

a(n) = +3*a(n-1) -3*a(n-2) +a(n-3) +a(n-11) -3*a(n-12) +3*a(n-13) -a(n-14). - R. J. Mathar, Apr 15 2010

G.f.: x^4*(2-x+x^2+2*x^3-2*x^4+2*x^5+x^6+x^9)/((1-x)^4*(1+x+x^2+x^3+x^4+x^5 +x^6+x^7+x^8+x^9+x^10)). - Peter J. C. Moses, Jun 02 2014

Extensions

a(41) onwards from G. C. Greubel, Oct 06 2024