A011890 a(n) = floor( n*(n-1)*(n-2)/8 ).

0, 0, 0, 0, 3, 7, 15, 26, 42, 63, 90, 123, 165, 214, 273, 341, 420, 510, 612, 726, 855, 997, 1155, 1328, 1518, 1725, 1950, 2193, 2457, 2740, 3045, 3371, 3720, 4092, 4488, 4908, 5355, 5827, 6327, 6854, 7410, 7995, 8610, 9255, 9933, 10642, 11385, 12161, 12972, 13818, 14700

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,0,0,0,1,-3,3,-1).

Crossrefs

Cf. A011886.

Programs

Magma

[Floor(6*Binomial(n,3)/8): n in [0..50]]; // G. C. Greubel, Oct 06 2024

Mathematica

Floor[6*Binomial[Range[0,50], 3]/8] (* G. C. Greubel, Oct 06 2024 *)

SageMath

[6*binomial(n,3)//8 for n in range(51)] # G. C. Greubel, Oct 06 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-8) -3*a(n-9) +3*a(n-10) -a(n-11).

G.f.: x^4*(3-2*x+3*x^2-x^3+2*x^4+x^6)/((1-x)^4*(1+x)*(1+x^2)*(1+x^4)). (End)

Extensions

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