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%I #23 May 03 2023 11:49:23
%S 0,0,0,0,1,2,5,10,16,24,34,47,62,81,104,130,160,194,233,276,325,380,
%T 440,506,578,657,742,835,936,1044,1160,1284,1417,1558,1709,1870,2040,
%U 2220,2410,2611,2822,3045,3280
%N a(n) = floor(n*(n-1)*(n-2)/21).
%H Vincenzo Librandi, <a href="/A011903/b011903.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1,0,0,0,1,-3,3,-1). [From _R. J. Mathar_, Apr 15 2010]
%F From _R. J. Mathar_, Apr 15 2010: (Start)
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-7) - 3*a(n-8) + 3*a(n-9) - a(n-10).
%F G.f.: x^4*(x^5-x^4+2*x^2-x+1) / ( (-1+x)^4*(x^6+x^5+x^4+x^3+x^2+x+1) ). (End)
%t CoefficientList[Series[x^4*(x^5-x^4+2*x^2-x+1)/((-1+x)^4*(x^6+x^5+x^4+ 5x^3+x^2+x+1)),{x,0,10}],x] (* _Vincenzo Librandi_, Jul 07 2012 *)
%t LinearRecurrence[{3,-3,1,0,0,0,1,-3,3,-1},{0,0,0,0,1,2,5,10,16,24},60] (* _Harvey P. Dale_, May 03 2023 *)
%o (Magma) [Floor(n*(n-1)*(n-2)/21): n in [0..50]]; // _Vincenzo Librandi_, Jul 07 2012
%K nonn,easy
%O 0,6
%A _N. J. A. Sloane_
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