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%I #18 Jun 13 2023 10:53:05
%S 0,0,0,1,4,12,24,42,67,100,144,198,264,343,436,546,672,816,979,1162,
%T 1368,1596,1848,2125,2428,2760,3120,3510,3931,4384,4872,5394,5952,
%U 6547,7180,7854,8568,9324,10123,10966
%N [ n(n-1)(n-2)/5 ].
%H Vincenzo Librandi, <a href="/A011887/b011887.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (3, -3, 1, 0, 1, -3, 3, -1).
%F a(n) = +3*a(n-1) -3*a(n-2) +a(n-3) +a(n-5) -3*a(n-6) +3*a(n-7) -a(n-8). G.f.: x^3*(1+x+3*x^2-x^3+2*x^4) / ( (-1+x)^4*(1+x+x^2+x^3+x^4) ). [From _R. J. Mathar_, Apr 15 2010]
%t CoefficientList[Series[x^3*(1+x+3*x^2-x^3+2*x^4)/((-1+x)^4*(1+x+x^2+x^3+x^4)),{x,0,50}],x] (* _Vincenzo Librandi_, Jul 07 2012 *)
%o (Magma) [Floor(n*(n-1)*(n-2)/5): n in [0..50]]; // _Vincenzo Librandi_, Jul 07 2012
%K nonn,easy
%O 0,5
%A _N. J. A. Sloane_.
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