This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A011886 #31 Oct 10 2024 05:25:51
%S A011886 0,0,0,1,6,15,30,52,84,126,180,247,330,429,546,682,840,1020,1224,1453,
%T A011886 1710,1995,2310,2656,3036,3450,3900,4387,4914,5481,6090,6742,7440,
%U A011886 8184,8976,9817,10710,11655,12654,13708,14820,15990,17220,18511,19866,21285
%N A011886 a(n) = floor(n*(n-1)*(n-2)/4).
%H A011886 Vincenzo Librandi, <a href="/A011886/b011886.txt">Table of n, a(n) for n = 0..1000</a>
%H A011886 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1,1,-3,3,-1).
%F A011886 From _R. J. Mathar_, Apr 15 2010: (Start)
%F A011886 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).
%F A011886 G.f.: x^3*(1+3*x+2*x^3) / ( (1-x)^4*(1+x)*(1+x^2) ). (End)
%F A011886 a(n) = floor(Sum_{k=0..n} n*(k+1)/2) for n >= -2. - _William A. Tedeschi_, Sep 10 2010
%t A011886 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 *)
%t A011886 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 *)
%o A011886 (Magma) [Floor(n*(n-1)*(n-2)/4): n in [0..50]]; // _Vincenzo Librandi_, Jul 07 2012
%o A011886 (SageMath) [3*binomial(n,3)//2 for n in range(51)] # _G. C. Greubel_, Oct 06 2024
%Y A011886 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).
%K A011886 nonn,easy
%O A011886 0,5
%A A011886 _N. J. A. Sloane_
%E A011886 More terms from _William A. Tedeschi_, Sep 10 2010