A158308 361n - 1.

360, 721, 1082, 1443, 1804, 2165, 2526, 2887, 3248, 3609, 3970, 4331, 4692, 5053, 5414, 5775, 6136, 6497, 6858, 7219, 7580, 7941, 8302, 8663, 9024, 9385, 9746, 10107, 10468, 10829, 11190, 11551, 11912, 12273, 12634, 12995, 13356, 13717, 14078

Offset

1,1

Comments

The identity (361*n-1)^2-(361*n^2-2*n)*(19)^2=1 can be written as a(n)^2-A158307(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 (2,-1).

Formula

G.f.: x*(360+x)/(1-x)^2.

a(1)=360, a(2)=721, a(n)=2*a(n-1)-a(n-2). - Harvey P. Dale, Aug 18 2011

Mathematica

361*Range[40]-1 (* or *) LinearRecurrence[{2, -1}, {360, 721}, 40] (* Harvey P. Dale, Aug 18 2011 *)

Prog

(Magma) I:=[360, 721]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n)=361*n-1

Crossrefs

Cf. A158307.

Sequence in context: A048978 A056502 A056492 * A205738 A112536 A140801

Adjacent sequences: A158305 A158306 A158307 * A158309 A158310 A158311

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 16 2009

Extensions

Minor corrections and edits by M. F. Hasler, Oct 14 2014

Status

approved