A158326 484n + 1.

485, 969, 1453, 1937, 2421, 2905, 3389, 3873, 4357, 4841, 5325, 5809, 6293, 6777, 7261, 7745, 8229, 8713, 9197, 9681, 10165, 10649, 11133, 11617, 12101, 12585, 13069, 13553, 14037, 14521, 15005, 15489, 15973, 16457, 16941, 17425, 17909

Offset

1,1

Comments

The identity (484*n+1)^2-(484*n^2+2*n)*(22)^2=1 can be written as a(n)^2-A158325(n)*(22)^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*(22^2*t+2)).

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

Formula

G.f.: x*(485-x)/(1-x)^2.

a(n) = 2*a(n-1)-a(n-2).

Mathematica

LinearRecurrence[{2, -1}, {485, 969}, 50]
484*Range[40]+1 (* Harvey P. Dale, Apr 29 2018 *)

Prog

(Magma) I:=[485, 969]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 484*n + 1.

Crossrefs

Cf. A158325.

Sequence in context: A114774 A013903 A160090 * A031722 A156774 A031632

Adjacent sequences: A158323 A158324 A158325 * A158327 A158328 A158329

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 16 2009

Status

approved