A158011 a(n) = 512n - 1.

511, 1023, 1535, 2047, 2559, 3071, 3583, 4095, 4607, 5119, 5631, 6143, 6655, 7167, 7679, 8191, 8703, 9215, 9727, 10239, 10751, 11263, 11775, 12287, 12799, 13311, 13823, 14335, 14847, 15359, 15871, 16383, 16895, 17407, 17919, 18431, 18943

Offset

1,1

Comments

The identity (512*n-1)^2 - (256*n^2 - n)*32^2 = 1 can be written as a(n)^2 - A158010(n)*32^2 = 1. - Vincenzo Librandi, Feb 10 2012

Links

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

E. J. Barbeau, Polynomial Excursions, Chapter 10: Diophantine equations (2010), pages 84-85 (row 14 in the first table at p. 85, case d(t) = t*(16^2*t-1)).

Index entries for linear recurrences with constant coefficients, signature (2, -1).

Formula

G.f.: x*(x+511)/(x-1)^2. - Vincenzo Librandi, Feb 10 2012

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Feb 10 2012

Mathematica

LinearRecurrence[{2, -1}, {511, 1023}, 50] (* Vincenzo Librandi, Feb 10 2012 *)

Prog

(Magma) I:=[511, 1023]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Feb 10 2012
(PARI) for(n=1, 50, print1(512*n - 1", ")); \\ Vincenzo Librandi, Feb 10 2012

Crossrefs

Cf. A158010.

Sequence in context: A023691 A045118 A043451 * A032656 A031899 A143036

Adjacent sequences: A158008 A158009 A158010 * A158012 A158013 A158014

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 11 2009

Status

approved