A158322 a(n) = 441*n + 1.

442, 883, 1324, 1765, 2206, 2647, 3088, 3529, 3970, 4411, 4852, 5293, 5734, 6175, 6616, 7057, 7498, 7939, 8380, 8821, 9262, 9703, 10144, 10585, 11026, 11467, 11908, 12349, 12790, 13231, 13672, 14113, 14554, 14995, 15436, 15877, 16318, 16759

Offset

1,1

Comments

The identity (441*n + 1)^2 - (441*n^2 + 2*n)*21^2 = 1 can be written as a(n)^2 - A158321(n)*21^2 = 1. - Vincenzo Librandi, Jan 24 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 15 in the first table at p. 85, case d(t) = t*(21^2*t+2)).

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

Formula

G.f.: x*(442-x)/(1-x)^2. - Vincenzo Librandi, Jan 24 2012

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jan 24 2012

Mathematica

LinearRecurrence[{2, -1}, {442, 883}, 50] (* Vincenzo Librandi, Jan 24 2012 *)

Prog

(Magma) I:=[442, 883]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) for(n=1, 38, print1(441*n+1", ")); \\ Vincenzo Librandi, Jan 24 2012

Crossrefs

Cf. A158321.

Sequence in context: A013899 A075268 A332531 * A031720 A069106 A094410

Adjacent sequences: A158319 A158320 A158321 * A158323 A158324 A158325

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 16 2009

Status

approved