A158253 289n - 1.

288, 577, 866, 1155, 1444, 1733, 2022, 2311, 2600, 2889, 3178, 3467, 3756, 4045, 4334, 4623, 4912, 5201, 5490, 5779, 6068, 6357, 6646, 6935, 7224, 7513, 7802, 8091, 8380, 8669, 8958, 9247, 9536, 9825, 10114, 10403, 10692, 10981, 11270, 11559

Offset

1,1

Comments

The identity (289*n-1)^2-(289*n^2-2*n)*(17)^2=1 can be written as a(n)^2-A158252(n)*(17)^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*(17^2*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*(288+x)/(1-x)^2.

Mathematica

289Range[50]-1 (* Harvey P. Dale, Nov 01 2011 *)
LinearRecurrence[{2, -1}, {288, 577}, 50]

Prog

(Magma) I:=[288, 577]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 289*n - 1.

Crossrefs

Cf. A158252.

Sequence in context: A250774 A082994 A127350 * A292054 A250788 A179646

Adjacent sequences: A158250 A158251 A158252 * A158254 A158255 A158256

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 15 2009

Status

approved