A158330 484n - 1.

483, 967, 1451, 1935, 2419, 2903, 3387, 3871, 4355, 4839, 5323, 5807, 6291, 6775, 7259, 7743, 8227, 8711, 9195, 9679, 10163, 10647, 11131, 11615, 12099, 12583, 13067, 13551, 14035, 14519, 15003, 15487, 15971, 16455, 16939, 17423, 17907

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-A158329(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

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

G.f.: x*(483+x)/(1-x)^2.

Mathematica

LinearRecurrence[{2, -1}, {483, 967}, 50]

Prog

(Magma) I:=[483, 967]; [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. A158329.

Sequence in context: A121734 A260976 A281047 * A288082 A251625 A156646

Adjacent sequences: A158327 A158328 A158329 * A158331 A158332 A158333

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 16 2009

Status

approved