A158250 a(n) = 256*n - 1.

255, 511, 767, 1023, 1279, 1535, 1791, 2047, 2303, 2559, 2815, 3071, 3327, 3583, 3839, 4095, 4351, 4607, 4863, 5119, 5375, 5631, 5887, 6143, 6399, 6655, 6911, 7167, 7423, 7679, 7935, 8191, 8447, 8703, 8959, 9215, 9471, 9727, 9983, 10239, 10495

Offset

1,1

Comments

The identity (256*n-1)^2 - (256*n^2 - 2*n)*16^2 = 1 can be written as a(n)^2 - A158249(n)*16^2 = 1.

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 15 in the first table at p. 85, case d(t) = t*(16^2*t-2)).

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

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

Formula

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

G.f.: x*(255 + x)/(1-x)^2.

E.g.f.: (-1 + 256*x)*exp(x). - G. C. Greubel, Apr 24 2022

Mathematica

LinearRecurrence[{2, -1}, {255, 511}, 50]

Prog

(Magma) I:=[255, 511]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 256*n - 1.
(SageMath) [256*n-1 for n in (1..50)] # G. C. Greubel, Apr 24 2022

Crossrefs

Cf. A158249.

Sequence in context: A043348 A031469 A045065 * A045137 A329489 A045113

Adjacent sequences: A158247 A158248 A158249 * A158251 A158252 A158253

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 15 2009

Status

approved