A011898 a(n) = floor(n*(n-1)*(n-2)/16).

0, 0, 0, 0, 1, 3, 7, 13, 21, 31, 45, 61, 82, 107, 136, 170, 210, 255, 306, 363, 427, 498, 577, 664, 759, 862, 975, 1096, 1228, 1370, 1522, 1685, 1860, 2046, 2244, 2454, 2677, 2913, 3163, 3427, 3705, 3997, 4305

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A011886.

Programs

Magma

[Floor(n*(n-1)*(n-2)/16): n in [0..50]]; // Vincenzo Librandi, May 21 2012

Mathematica

Table[Floor[(n(n-1)(n-2))/16],{n,0,50}] (* Harvey P. Dale, May 16 2012 *)

PARI

a(n) = n*(n-1)*(n-2)\16; \\ Michel Marcus, Jan 14 2018

SageMath

[3*binomial(n,3)//8 for n in range(51)] # G. C. Greubel, Oct 16 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-16) - 3*a(n-17) + 3*a(n-18) - a(n-19).

G.f.: x^4*(1+x^2+2*x^6-2*x^7+3*x^8-x^9+x^11+x^12-x^13+x^14) / ( (1-x)^4*(1+x)*(1+x^2)*(1+x^4)*(1+x^8) ). (End)