A157958 a(n) = 242*n + 1.

243, 485, 727, 969, 1211, 1453, 1695, 1937, 2179, 2421, 2663, 2905, 3147, 3389, 3631, 3873, 4115, 4357, 4599, 4841, 5083, 5325, 5567, 5809, 6051, 6293, 6535, 6777, 7019, 7261, 7503, 7745, 7987, 8229, 8471, 8713, 8955, 9197, 9439, 9681, 9923, 10165

Offset

1,1

Comments

The identity (242*n + 1)^2 - (121*n^2 + n)*22^2 = 1 can be written as a(n)^2 - A173267(n)*22^2 = 1. - Vincenzo Librandi, Feb 06 2012

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*(11^2*t+1)).

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

Formula

G.f.: x*(243-x)/(1-x)^2. - Vincenzo Librandi, Feb 06 2012

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Feb 06 2012

Mathematica

LinearRecurrence[{2, -1}, {243, 485}, 50] (* Vincenzo Librandi, Feb 06 2012 *)
242*Range[50]+1 (* Harvey P. Dale, Sep 01 2015 *)

Prog

(Magma) I:=[243, 485]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Feb 06 2012
(PARI) for(n=1, 40, print1(242*n + 1", ")); \\ Vincenzo Librandi, Feb 06 2012

Crossrefs

Cf. A173267.

Sequence in context: A046318 A046375 A226064 * A232924 A067838 A340757

Adjacent sequences: A157955 A157956 A157957 * A157959 A157960 A157961

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 10 2009

Status

approved