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

0,1

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).

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A004782 A049956 A289844 * A235112 A081207 A353580

Adjacent sequences: A153053 A153054 A153055 * A153057 A153058 A153059

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Dec 17 2008

Status

approved