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

Offset

1,2

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).

Formula

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

Mathematica

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

Prog

(Magma) [8*n^2 - 6*n - 1: n in [1..50]]; // Vincenzo Librandi, Sep 07 2011
(PARI) a(n)=8*n^2-6*n-1 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

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

Sequence in context: A118591 A031341 A165982 * A024848 A240136 A072581

Adjacent sequences: A194428 A194429 A194430 * A194432 A194433 A194434

Keyword

nonn,easy

Author

Omar E. Pol, Sep 05 2011

Status

approved