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

0,5

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).

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

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 *)

Prog

(Magma) [Floor(6*Binomial(n, 3)/11): n in [0..50]]; // G. C. Greubel, Oct 06 2024
(SageMath) [6*binomial(n, 3)//11 for n in range(51)] # G. C. Greubel, Oct 06 2024

Crossrefs

Cf. A011886.

Sequence in context: A018739 A325648 A325718 * A132210 A000098 A024827

Adjacent sequences: A011890 A011891 A011892 * A011894 A011895 A011896

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

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

Status

approved