A194431 a(n) = 8*n^2 - 6*n - 1.

1, 19, 53, 103, 169, 251, 349, 463, 593, 739, 901, 1079, 1273, 1483, 1709, 1951, 2209, 2483, 2773, 3079, 3401, 3739, 4093, 4463, 4849, 5251, 5669, 6103, 6553, 7019, 7501, 7999, 8513, 9043, 9589, 10151, 10729, 11323, 11933, 12559, 13201, 13859, 14533, 15223, 15929

Offset: 1

Author

Omar E. Pol, Sep 05 2011

Keywords

• nonn
• easy

Comments

Sequence found by reading the line from 1, in the direction 1, 19, ..., in the square spiral whose vertices are the triangular numbers A000217.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A000217, A014634, A051870, A069129, A139098, A194268.

Programs

Magma

[8*n^2 - 6*n - 1: n in [1..50]]; // Vincenzo Librandi, Sep 07 2011

Mathematica

Table[8n^2-6n-1,{n,50}] (* or *) LinearRecurrence[{3,-3,1},{1,19,53},50] (* Harvey P. Dale, May 29 2021 *)

PARI

a(n)=8*n^2-6*n-1 \\ Charles R Greathouse IV, Oct 07 2015

Formula

G.f.: x*(-1 - 16*x + x^2)/(x-1)^3. - R. J. Mathar, Sep 06 2011

From Elmo R. Oliveira, Jun 04 2025: (Start)

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

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