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%I #21 Sep 06 2023 09:46:50
%S 2,3,7,16,32,57,93,142,206,287,387,508,652,821,1017,1242,1498,1787,
%T 2111,2472,2872,3313,3797,4326,4902,5527,6203,6932,7716,8557,9457,
%U 10418,11442,12531,13687,14912,16208,17577,19021,20542,22142,23823,25587
%N a(0)=2, a(n) = n^2+a(n-1).
%H Shawn A. Broyles, <a href="/A153056/b153056.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 G.f.: (2-5x+7x^2-2x^3)/(1-x)^4. a(n)=2+n(1+2n^2+3n)/6 = 2+A000330(n). - _R. J. Mathar_, Jan 08 2009
%t a=2;lst={};Do[a=n^2+a;AppendTo[lst,a],{n,0,5!}];lst
%t nxt[{n_,a_}]:={n+1,(n+1)^2+a}; NestList[nxt,{0,2},50][[;;,2]] (* or *) LinearRecurrence[{4,-6,4,-1},{2,3,7,16},50] (* _Harvey P. Dale_, Sep 05 2023 *)
%o (PARI) a(n) = n*(n+1)*(2*n+1)/6 + 2; \\ _Altug Alkan_, Apr 30 2018
%Y Cf. A000330, A056520, A153057, A153058, A179904.
%K nonn,easy
%O 0,1
%A _Vladimir Joseph Stephan Orlovsky_, Dec 17 2008
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