A096376 a(n) = n + (n-1)^2 + (n+1)^2.

2, 5, 12, 23, 38, 57, 80, 107, 138, 173, 212, 255, 302, 353, 408, 467, 530, 597, 668, 743, 822, 905, 992, 1083, 1178, 1277, 1380, 1487, 1598, 1713, 1832, 1955, 2082, 2213, 2348, 2487, 2630, 2777, 2928, 3083, 3242, 3405, 3572, 3743, 3918, 4097, 4280, 4467, 4658

Offset

0,1

Comments

Numbers represented as 212 in number base n including binary with digits larger than 1: 212_2 = 12 and ternary 212_3 = 23. - Ron Knott, Nov 14 2017

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

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

Formula

a(n) = 2*n^2 + n + 2. - N. J. A. Sloane, Nov 10 2009

a(n) = 4*n + a(n-1) - 1 (with a(0)=2). - Vincenzo Librandi, Nov 16 2010

From Colin Barker, Oct 03 2012: (Start)

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

G.f.: (2 - x + 3*x^2)/(1-x)^3. (End)

E.g.f.: (2*x^2 + 3*x +2)*exp(x). - G. C. Greubel, Jul 16 2017

Example

1 + 0 + 4 = 5, 2 + 1 + 9 = 12, 3 + 4 + 16 = 23, ...

Maple

A096376:=n->n + (n-1)^2 + (n+1)^2: seq(A096376(n), n=0..100); # Wesley Ivan Hurt, Jul 16 2017

Mathematica

f[n_]:=(n*(2*n+1)+2); Table[f[n], {n, 5!}] (* Vladimir Joseph Stephan Orlovsky, Feb 07 2010 *)
LinearRecurrence[{3, -3, 1}, {2, 5, 12}, 50] (* Harvey P. Dale, Mar 15 2015 *)

Prog

(PARI) a(n)=n+(n-1)^2+(n+1)^2 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Sequence in context: A109653 A115520 A116735 * A357288 A326510 A112287

Adjacent sequences: A096373 A096374 A096375 * A096377 A096378 A096379

Keyword

easy,nonn

Author

Odimar Fabeny, Aug 04 2004

Status

approved