A157999 a(n) = 338n - 1.

337, 675, 1013, 1351, 1689, 2027, 2365, 2703, 3041, 3379, 3717, 4055, 4393, 4731, 5069, 5407, 5745, 6083, 6421, 6759, 7097, 7435, 7773, 8111, 8449, 8787, 9125, 9463, 9801, 10139, 10477, 10815, 11153, 11491, 11829, 12167, 12505, 12843, 13181, 13519

Offset

1,1

Comments

The identity (338*n-1)^2-(169*n^2-n)*(26)^2=1 can be written as a(n)^2-A157998(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 14 in the first table at p. 85, case d(t) = t*(13^2*t-1)).

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

Formula

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

G.f.: x*(337+x)/(1-x)^2.

Mathematica

LinearRecurrence[{2, -1}, {337, 675}, 50]
338*Range[40]-1 (* Harvey P. Dale, Jun 04 2019 *)

Prog

(Magma) I:=[337, 675]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 338*n - 1.

Crossrefs

Cf. A157998.

Sequence in context: A051962 A339480 A214492 * A152853 A142830 A160069

Adjacent sequences: A157996 A157997 A157998 * A158000 A158001 A158002

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 11 2009

Status

approved