A011902 a(n) = floor( n*(n-1)*(n-2)/20 ).

0, 0, 0, 0, 1, 3, 6, 10, 16, 25, 36, 49, 66, 85, 109, 136, 168, 204, 244, 290, 342, 399, 462, 531, 607, 690, 780, 877, 982, 1096, 1218, 1348, 1488, 1636, 1795, 1963, 2142, 2331, 2530, 2741, 2964, 3198, 3444, 3702, 3973, 4257, 4554, 4864, 5188, 5527, 5880, 6247, 6630, 7027, 7441, 7870, 8316, 8778, 9256, 9752, 10266, 10797, 11346, 11913, 12499, 13104, 13728, 14371

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,-3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-3,3,-1).

Crossrefs

Cf. A011886.

Programs

Magma

[Floor(3*Binomial(n,3)/10): n in [0..80]]; // G. C. Greubel, Oct 18 2024

Mathematica

Table[Floor[(n(n-1)(n-2))/20],{n,0,80}]  (* Harvey P. Dale, Mar 23 2011 *)

SageMath

[3*binomial(n,3)//10 for n in range(81)] # G. C. Greubel, Oct 18 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-20) -3*a(n-21) +3*a(n-22) -a(n-23).

G.f.: x^4*(1+x^4+x^5-x^6+2*x^8-2*x^9+3*x^10-2*x^11+2*x^12-x^13+2*x^15-x^17+x^18)/((1-x)^4*(1+x)*(1+x^2)*(1+x+x^2+x^3+x^4)*(1-x+x^2-x^3+x^4)*(1-x^2+x^4-x^6+x^8)). (End)

Extensions

More terms added by G. C. Greubel, Oct 18 2024