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A153057 a(0)=3; a(n) = n^2 + a(n-1) for n>0.

%I A153057 #18 Sep 06 2023 09:47:18
%S A153057 3,4,8,17,33,58,94,143,207,288,388,509,653,822,1018,1243,1499,1788,
%T A153057 2112,2473,2873,3314,3798,4327,4903,5528,6204,6933,7717,8558,9458,
%U A153057 10419,11443,12532,13688,14913,16209,17578,19022,20543,22143,23824,25588
%N A153057 a(0)=3; a(n) = n^2 + a(n-1) for n>0.
%H A153057 Vincenzo Librandi, <a href="/A153057/b153057.txt">Table of n, a(n) for n = 0..1000</a>
%H A153057 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A153057 From _R. J. Mathar_, Jan 17 2009: (Start)
%F A153057 G.f.: (3-8*x + 10*x^2 - 3*x^3)/(1 - x)^4.
%F A153057 a(n) = 3+A000330(n). (End)
%F A153057 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - _Vincenzo Librandi_, May 09 2017
%t A153057 a=3;lst={};Do[a=n^2+a;AppendTo[lst,a],{n,0,5!}];lst
%t A153057 CoefficientList[Series[(3 - 8 x + 10 x^2 - 3 x^3) / (1 - x)^4, {x, 0, 50}], x] (* _Vincenzo Librandi_, May 09 2017 *)
%o A153057 (Magma) I:=[3,4,8,17]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..60]]; // _Vincenzo Librandi_, May 09 2017
%Y A153057 Cf. A000330, A056520, A153056, A153058, A179904.
%K A153057 nonn,easy
%O A153057 0,1
%A A153057 _Vladimir Joseph Stephan Orlovsky_, Dec 17 2008
%E A153057 Added indices to definition. Corrected offset _R. J. Mathar_, Jan 17 2009