A106648 a(n) = 3*n^2 + 6*n + 8.

8, 17, 32, 53, 80, 113, 152, 197, 248, 305, 368, 437, 512, 593, 680, 773, 872, 977, 1088, 1205, 1328, 1457, 1592, 1733, 1880, 2033, 2192, 2357, 2528, 2705, 2888, 3077, 3272, 3473, 3680, 3893, 4112, 4337, 4568, 4805, 5048, 5297, 5552, 5813, 6080, 6353, 6632

Offset

0,1

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(0)=8, a(1)=17, a(2)=32, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - Harvey P. Dale, Sep 20 2012

G.f.: (8 -7*x +5*x^2)/(1-x)^3. - R. J. Mathar, Nov 07 2015

E.g.f.: (8 +9*x +3*x^2)*exp(x). - G. C. Greubel, Sep 08 2021

Mathematica

Table[3n^2+6n+8, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {8, 17, 32}, 50] (* Harvey P. Dale, Sep 20 2012 *)

Prog

(PARI) a(n)=3*n^2+6*n+8 \\ Charles R Greathouse IV, Jun 17 2017
(Sage) [3*(n+1)^2 + 5 for n in (0..50)] # G. C. Greubel, Sep 08 2021

Crossrefs

Sequence in context: A077222 A077221 A226601 * A209376 A159696 A049713

Adjacent sequences: A106645 A106646 A106647 * A106649 A106650 A106651

Keyword

nonn,easy

Author

MICK JOYCE (mjpj69(AT)msn.com), Jan 22 2006

Extensions

Definition supplied by Joshua Zucker, Feb 01, 2006

Status

approved