A158227 a(n) = 225*n - 1.

224, 449, 674, 899, 1124, 1349, 1574, 1799, 2024, 2249, 2474, 2699, 2924, 3149, 3374, 3599, 3824, 4049, 4274, 4499, 4724, 4949, 5174, 5399, 5624, 5849, 6074, 6299, 6524, 6749, 6974, 7199, 7424, 7649, 7874, 8099, 8324, 8549, 8774, 8999, 9224, 9449, 9674

Offset

1,1

Comments

The identity (225*n-1)^2-(225*n^2-2*n)*(15)^2=1 can be written as a(n)^2-A158226(n)*(15)^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*(15^2*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*(224+x)/(1-x)^2.

Mathematica

LinearRecurrence[{2, -1}, {224, 449}, 50]
225*Range[50]-1 (* Harvey P. Dale, Feb 27 2023 *)

Prog

(Magma) I:=[224, 449]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 225*n - 1.

Crossrefs

Cf. A158226.

Sequence in context: A202442 A331371 A094209 * A061524 A156813 A233875

Adjacent sequences: A158224 A158225 A158226 * A158228 A158229 A158230

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 14 2009

Status

approved