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A011842 a(n) = floor(n*(n-1)*(n-2)/24).

%I A011842 #24 Oct 21 2024 04:36:26
%S A011842 0,0,0,0,1,2,5,8,14,21,30,41,55,71,91,113,140,170,204,242,285,332,385,
%T A011842 442,506,575,650,731,819,913,1015,1123,1240,1364,1496,1636,1785,1942,
%U A011842 2109,2284,2470,2665,2870,3085,3311,3547,3795,4053,4324,4606,4900,5206,5525,5856,6201,6558,6930,7315,7714,8127,8555,8997,9455,9927,10416,10920
%N A011842 a(n) = floor(n*(n-1)*(n-2)/24).
%H A011842 G. C. Greubel, <a href="/A011842/b011842.txt">Table of n, a(n) for n = 0..2000</a>
%H A011842 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1,0,0,0,0,1,-3,3,-1).
%F A011842 From _R. J. Mathar_, Apr 15 2010: (Start)
%F A011842 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-8) - 3*a(n-9) + 3*a(n-10) - a(n-11).
%F A011842 G.f.: x^4*(1-x+x^2)*(1+x^2-x^3+x^4) / ((1-x)^4*(1+x)*(1+x^2)*(1+x^4)). (End)
%F A011842 a(n) = floor(binomial(n+1,4)/(n+1)). - _Gary Detlefs_, Nov 23 2011
%p A011842 seq(floor(binomial(n,3)/4), n=0..43); # _Zerinvary Lajos_, Jan 12 2009
%t A011842 Floor[Binomial[Range[0,80], 3]/4] (* _G. C. Greubel_, Oct 20 2024 *)
%o A011842 (Magma) [Floor(Binomial(n,3)/4): n in [0..80]]; // _G. C. Greubel_, Oct 20 2024
%o A011842 (SageMath) [binomial(n,3)//4 for n in range(81)] # _G. C. Greubel_, Oct 20 2024
%Y A011842 A column of triangle A011847.
%Y A011842 Cf. A011886.
%K A011842 nonn
%O A011842 0,6
%A A011842 _N. J. A. Sloane_
%E A011842 More terms added by _G. C. Greubel_, Oct 20 2024