A158307 361n^2 - 2n.

359, 1440, 3243, 5768, 9015, 12984, 17675, 23088, 29223, 36080, 43659, 51960, 60983, 70728, 81195, 92384, 104295, 116928, 130283, 144360, 159159, 174680, 190923, 207888, 225575, 243984, 263115, 282968, 303543, 324840, 346859, 369600

Offset

1,1

Comments

The identity (361*n-1)^2-(361*n^2-2*n)*(19)^2=1 can be written as A158308(n)^2-a(n)*(19)^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*(19^2*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*(-359-363*x)/(x-1)^3.

Mathematica

LinearRecurrence[{3, -3, 1}, {359, 1440, 3243}, 50]

Prog

(Magma) I:=[359, 1440, 3243]; [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) = 361*n^2 - 2*n.

Crossrefs

Cf. A158308.

Sequence in context: A101796 A175537 A142852 * A013325 A344284 A179678

Adjacent sequences: A158304 A158305 A158306 * A158308 A158309 A158310

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 16 2009

Status

approved