A011909 a(n) = floor( n*(n-1)*(n-2)/27 ).

0, 0, 0, 0, 0, 2, 4, 7, 12, 18, 26, 36, 48, 63, 80, 101, 124, 151, 181, 215, 253, 295, 342, 393, 449, 511, 577, 650, 728, 812, 902, 998, 1102, 1212, 1329, 1454, 1586, 1726, 1874, 2030, 2195, 2368, 2551, 2742, 2943, 3153, 3373, 3603, 3843, 4094, 4355, 4627, 4911, 5205, 5512, 5830, 6160, 6502, 6856, 7224, 7604, 7997, 8404, 8824, 9258, 9706, 10168, 10645, 11136

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..2000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,3,3,-6,3,3,-6,3,3,-6,3,3,-6,3,3,-6,3,3,-6,3,3,-6,3,3,-6,4,-1).

Crossrefs

Cf. A011886.

Programs

Magma

[Floor(2*Binomial(n,3)/9): n in [0..80]]; // G. C. Greubel, Oct 19 2024

Mathematica

Table[Floor[n(n-1)(n-2)/27],{n,0,80}] (* or *)
LinearRecurrence[{4,-6,3,3,-6,3,3,-6,3,3,-6,3,3,-6,3,3,-6,3,3,-6,3,3,-6,3,3,-6,4,-1},{0,0,0,0,0,2,4,7,12,18,26,36,48,63,80,101,124,151,181,215,253,295, 342,393,449,511,577,650}, 81] (* Harvey P. Dale, Jun 12 2023 *)

SageMath

[2*binomial(n,3)//9 for n in range(81)] # G. C. Greubel, Oct 19 2024

Formula

G.f.: x^5*(1-x+x^2)*(2-2*x-x^2+3*x^3-2*x^4+3*x^6-3*x^7+2*x^9-x^10-x^11 +3*x^12-2*x^13-x^14+3*x^15-2*x^16+2*x^18-2*x^19+x^20)/((1-x)^4*(1+x^3+x^6)*(1+x^9+x^18)). - Peter J. C. Moses, Jun 02 2014

Extensions

More terms added by G. C. Greubel, Oct 19 2024