A194268 a(n) = 8*n^2 + 7*n + 1.

1, 16, 47, 94, 157, 236, 331, 442, 569, 712, 871, 1046, 1237, 1444, 1667, 1906, 2161, 2432, 2719, 3022, 3341, 3676, 4027, 4394, 4777, 5176, 5591, 6022, 6469, 6932, 7411, 7906, 8417, 8944, 9487, 10046, 10621, 11212, 11819, 12442, 13081, 13736, 14407, 15094, 15797

Offset

0,2

Comments

Sequence found by reading the line from 1, in the direction 1, 16,..., in the square spiral whose vertices are the triangular numbers A000217.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

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

Formula

a(0)=1, a(1)=16, a(2)=47, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Apr 06 2014

From Elmo R. Oliveira, Oct 22 2024: (Start)

G.f.: (1 + 13*x + 2*x^2)/(1 - x)^3.

E.g.f.: (1 + 15*x + 8*x^2)*exp(x). (End)

Maple

A194268:=n->8*n^2+7*n+1: seq(A194268(n), n=0..50); # Wesley Ivan Hurt, Jul 15 2014

Mathematica

Table[8n^2+7n+1, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 16, 47}, 50] (* Harvey P. Dale, Apr 06 2014 *)

Prog

(Magma) [8*n^2 +7*n + 1: n in [0..50]]; // Vincenzo Librandi, Sep 07 2011
(PARI) a(n)=8*n^2+7*n+1 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A000217, A014634, A051870, A069129, A139098, A194431.

Sequence in context: A253350 A204616 A204800 * A292171 A204609 A233063

Adjacent sequences: A194265 A194266 A194267 * A194269 A194270 A194271

Keyword

nonn,easy

Author

Omar E. Pol, Sep 05 2011

Status

approved