A153056 a(0)=2, a(n) = n^2+a(n-1).

2, 3, 7, 16, 32, 57, 93, 142, 206, 287, 387, 508, 652, 821, 1017, 1242, 1498, 1787, 2111, 2472, 2872, 3313, 3797, 4326, 4902, 5527, 6203, 6932, 7716, 8557, 9457, 10418, 11442, 12531, 13687, 14912, 16208, 17577, 19021, 20542, 22142, 23823, 25587

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, Dec 17 2008

Keywords

• nonn
• easy

Links

• Shawn A. Broyles, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A000330, A056520, A153057, A153058, A179904.

Programs

Mathematica

a=2;lst={};Do[a=n^2+a;AppendTo[lst,a],{n,0,5!}];lst
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 *)

PARI

a(n) = n*(n+1)*(2*n+1)/6 + 2; \\ Altug Alkan, Apr 30 2018

Formula

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