A011886 a(n) = floor(n*(n-1)*(n-2)/4).

0, 0, 0, 1, 6, 15, 30, 52, 84, 126, 180, 247, 330, 429, 546, 682, 840, 1020, 1224, 1453, 1710, 1995, 2310, 2656, 3036, 3450, 3900, 4387, 4914, 5481, 6090, 6742, 7440, 8184, 8976, 9817, 10710, 11655, 12654, 13708, 14820, 15990, 17220, 18511, 19866, 21285

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

Crossrefs

Sequences of the form floor(n*(n-1)*(n-2)/m): A007531 (m=1), A135503 (m=2), A007290 (m=3), this sequence (m=4), A011887 (m=5), A000292 (m=6), A011889 (m=7), A011890 (m=8), A011891 (m=9), A011892 (m=10), A011893 (m=11), A011894 (m=12), A011895 (m=13), A011896 (m=14), A011897 (m=15), A011898 (m=16), A011899 (m=17), A011849 (m=18), A011901 (m=19), A011902 (m=20), A011903 (m=21), A011904 (m=22), A011905 (m=23), A011842 (m=24), A011907 (m=25), A011908 (m=26), A011909 (m=27), A011910 (m=28), A011911 (m=29), A011912 (m=30), A011912 (m=31), A011913 (m=32).

Programs

Magma

[Floor(n*(n-1)*(n-2)/4): n in [0..50]]; // Vincenzo Librandi, Jul 07 2012

Mathematica

Table[Floor[(n(n-1)(n-2))/4],{n,0,50}] (* or *) LinearRecurrence[{3,-3,1,1, -3,3,-1},{0,0,0,1,6,15,30}, 50] (* Harvey P. Dale, Feb 25 2012 *)
CoefficientList[Series[x^3*(1+3*x+2*x^3)/((1-x)^3*(1-x^4)),{x,0,50}],x] (* Vincenzo Librandi, Jul 07 2012 *)

SageMath

[3*binomial(n,3)//2 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-4) -3*a(n-5) +3*a(n-6) -a(n-7).

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

a(n) = floor(Sum_{k=0..n} n*(k+1)/2) for n >= -2. - William A. Tedeschi, Sep 10 2010

Extensions

More terms from William A. Tedeschi, Sep 10 2010