A158410 a(n) = 961*n^2 - 2*n.

959, 3840, 8643, 15368, 24015, 34584, 47075, 61488, 77823, 96080, 116259, 138360, 162383, 188328, 216195, 245984, 277695, 311328, 346883, 384360, 423759, 465080, 508323, 553488, 600575, 649584, 700515, 753368, 808143, 864840, 923459, 984000

Offset

1,1

Comments

The identity (961*n-1)^2-(961*n^2-2*n)*(31)^2 = 1 can be written as A158412(n)^2-a(n)*(31)^2 = 1.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Vincenzo Librandi, X^2-AY^2=1

E. J. Barbeau, Polynomial Excursions, Chapter 10: Diophantine equations (2010), pages 84-85 (row 15 in the first table at p. 85, case d(t) = t*(31^2*t-2)).

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

Formula

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

G.f.: x*(-959-963*x)/(x-1)^3.

Mathematica

LinearRecurrence[{3, -3, 1}, {959, 3840, 8643}, 50]
Table[961n^2-2n, {n, 40}] (* Harvey P. Dale, Aug 29 2022 *)

Prog

(Magma) I:=[959, 3840, 8643]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]];
(PARI) a(n) = 961*n^2 - 2*n.

Crossrefs

Cf. A158412.

Sequence in context: A031903 A226851 A351674 * A108903 A167780 A316338

Adjacent sequences: A158407 A158408 A158409 * A158411 A158412 A158413

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 18 2009

Status

approved