A157997 288n - 1.

287, 575, 863, 1151, 1439, 1727, 2015, 2303, 2591, 2879, 3167, 3455, 3743, 4031, 4319, 4607, 4895, 5183, 5471, 5759, 6047, 6335, 6623, 6911, 7199, 7487, 7775, 8063, 8351, 8639, 8927, 9215, 9503, 9791, 10079, 10367, 10655, 10943, 11231, 11519

Offset

1,1

Comments

The identity (288*n-1)^2-(144*n^2-n)*(24)^2=1 can be written as a(n)^2-A156635(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 14 in the first table at p. 85, case d(t) = t*(12^2*t-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*(287+x)/(1-x)^2.

Mathematica

LinearRecurrence[{2, -1}, {287, 575}, 50]
288*Range[40]-1 (* Harvey P. Dale, Aug 24 2019 *)

Prog

(Magma) I:=[287, 575]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 288*n - 1.

Crossrefs

Cf. A156635.

Sequence in context: A203049 A306788 A259402 * A063362 A159949 A158252

Adjacent sequences: A157994 A157995 A157996 * A157998 A157999 A158000

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 11 2009

Status

approved