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a(0)=3; a(n) = n^2 + a(n-1) for n>0.
6

%I #18 Sep 06 2023 09:47:18

%S 3,4,8,17,33,58,94,143,207,288,388,509,653,822,1018,1243,1499,1788,

%T 2112,2473,2873,3314,3798,4327,4903,5528,6204,6933,7717,8558,9458,

%U 10419,11443,12532,13688,14913,16209,17578,19022,20543,22143,23824,25588

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

%H Vincenzo Librandi, <a href="/A153057/b153057.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F From _R. J. Mathar_, Jan 17 2009: (Start)

%F G.f.: (3-8*x + 10*x^2 - 3*x^3)/(1 - x)^4.

%F a(n) = 3+A000330(n). (End)

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - _Vincenzo Librandi_, May 09 2017

%t a=3;lst={};Do[a=n^2+a;AppendTo[lst,a],{n,0,5!}];lst

%t CoefficientList[Series[(3 - 8 x + 10 x^2 - 3 x^3) / (1 - x)^4, {x, 0, 50}], x] (* _Vincenzo Librandi_, May 09 2017 *)

%o (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 Cf. A000330, A056520, A153056, A153058, A179904.

%K nonn,easy

%O 0,1

%A _Vladimir Joseph Stephan Orlovsky_, Dec 17 2008

%E Added indices to definition. Corrected offset _R. J. Mathar_, Jan 17 2009