A158231 a(n) = 256*n + 1.

257, 513, 769, 1025, 1281, 1537, 1793, 2049, 2305, 2561, 2817, 3073, 3329, 3585, 3841, 4097, 4353, 4609, 4865, 5121, 5377, 5633, 5889, 6145, 6401, 6657, 6913, 7169, 7425, 7681, 7937, 8193, 8449, 8705, 8961, 9217, 9473, 9729, 9985, 10241, 10497

Offset: 1

Author

Vincenzo Librandi, Mar 14 2009

Keywords

• nonn
• easy

Comments

The identity (256*n + 1)^2 - (256*n^2 + 2*n)*16^2 = 1 can be written as a(n)^2 - A158230(n)*16^2 = 1.

Also the identity (512*n + 1)^2 - (256*n^2 + n)*32^2 = 1 can be written as A076338(n)^2 - (n*a(n))*32^2 = 1. - Vincenzo Librandi, Feb 23 2012

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 (first identity in the comment section: row 15 in the initial table at p. 85, case d(t) = t*(16^2*t+2)).
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A076338, A158230.

Programs

Magma

I:=[257, 513]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];

Maple

A158231:=n->256*n + 1; seq(A158231(n), n=1..50); # Wesley Ivan Hurt, Jan 24 2014

Mathematica

256Range[50]+1 (* or *) LinearRecurrence[{2,-1},{257,513},50] (* Harvey P. Dale, Nov 21 2011 *)

PARI

a(n) = 256*n + 1

Formula

a(n) = 2*a(n-1) - a(n-2); a(1)=257, a(2)=513. - Harvey P. Dale, Nov 21 2011

G.f.: x*(257-x)/(x-1)^2. - Harvey P. Dale, Nov 21 2011