A158393 a(n) = 676*n - 1.

675, 1351, 2027, 2703, 3379, 4055, 4731, 5407, 6083, 6759, 7435, 8111, 8787, 9463, 10139, 10815, 11491, 12167, 12843, 13519, 14195, 14871, 15547, 16223, 16899, 17575, 18251, 18927, 19603, 20279, 20955, 21631, 22307, 22983, 23659, 24335

Offset

1,1

Comments

The identity (676*n-1)^2-(676*n^2-2*n)*(26)^2=1 can be written as a(n)^2-A158392(n)*(26)^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*(26^2*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*(675+x)/(1-x)^2.

Mathematica

LinearRecurrence[{2, -1}, {675, 1351}, 50]

Prog

(Magma) I:=[675, 1351]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 676*n - 1.

Crossrefs

Cf. A158392.

Sequence in context: A158392 A264328 A124942 * A294949 A159208 A358174

Adjacent sequences: A158390 A158391 A158392 * A158394 A158395 A158396

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 18 2009

Status

approved