A158372 576n - 1.

575, 1151, 1727, 2303, 2879, 3455, 4031, 4607, 5183, 5759, 6335, 6911, 7487, 8063, 8639, 9215, 9791, 10367, 10943, 11519, 12095, 12671, 13247, 13823, 14399, 14975, 15551, 16127, 16703, 17279, 17855, 18431, 19007, 19583, 20159, 20735, 21311

Offset

1,1

Comments

The identity (576*n-1)^2-(576*n^2-2*n)*(24)^2=1 can be written as a(n)^2-A158371(n)*(24)^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*(24^2*t-2)).

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

Formula

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

G.f.: x*(575+x)/(1-x)^2.

Mathematica

LinearRecurrence[{2, -1}, {575, 1151}, 50]
576*Range[40]-1 (* Harvey P. Dale, Dec 15 2017 *)

Prog

(Magma) I:=[575, 1151]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 576*n - 1.

Crossrefs

Cf. A158371.

Sequence in context: A369625 A291133 A027456 * A230353 A233482 A027527

Adjacent sequences: A158369 A158370 A158371 * A158373 A158374 A158375

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 17 2009

Status

approved