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

Author

Omar E. Pol, Sep 05 2011

Keywords

• nonn
• easy

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).

Crossrefs

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

Programs

Magma

[8*n^2 +7*n + 1: n in [0..50]]; // Vincenzo Librandi, Sep 07 2011

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 *)

PARI

a(n)=8*n^2+7*n+1 \\ Charles R Greathouse IV, Oct 07 2015

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)