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%I #21 Jul 21 2017 02:32:15
%S 0,23,52,87,128,175,228,287,352,423,500,583,672,767,868,975,1088,1207,
%T 1332,1463,1600,1743,1892,2047,2208,2375,2548,2727,2912,3103,3300,
%U 3503,3712,3927,4148,4375,4608,4847,5092,5343,5600,5863
%N a(n) = n*(3*n + 20).
%H Harvey P. Dale, <a href="/A140689/b140689.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = 3*n^2 + 20*n.
%F a(n) = a(n-1) + 6*n + 17 (with a(0)=0). - _Vincenzo Librandi_, Dec 15 2010
%F a(n) = 3*a(n-1)-3*a(n-2)+a(n-3), with a(0)=0, a(1)=23, a(2)=52. - _Harvey P. Dale_, Apr 29 2016
%F From _G. C. Greubel_, Jul 21 2017: (Start)
%F G.f.: x*(23 - 17*x)/(1 - x)^3.
%F E.g.f.: x*(3*x + 23)*exp(x). (End)
%t a[n_]:=Sum[6*i+17, {i, 1, n}]; (* _Vladimir Joseph Stephan Orlovsky_, Dec 04 2008 *)
%t Table[n(3n+20),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,23,52},50] (* _Harvey P. Dale_, Apr 29 2016 *)
%o (PARI) a(n)=n*(3*n+20) \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. A033428, A045944, A140676, A067725, A140677, A140678, A067707, A140679, A140680, A140681.
%K easy,nonn
%O 0,2
%A _Omar E. Pol_, May 22 2008
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