A158000 a(n) = 338*n + 1.

339, 677, 1015, 1353, 1691, 2029, 2367, 2705, 3043, 3381, 3719, 4057, 4395, 4733, 5071, 5409, 5747, 6085, 6423, 6761, 7099, 7437, 7775, 8113, 8451, 8789, 9127, 9465, 9803, 10141, 10479, 10817, 11155, 11493, 11831, 12169, 12507, 12845, 13183, 13521

Offset

1,1

Comments

The identity (338*n + 1)^2 - (169*n^2 + n)*26^2 = 1 can be written as a(n)^2 - A173275(n)*26^2 = 1. - Vincenzo Librandi, Feb 10 2012

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

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

G.f.: x*(339-x)/(1-x)^2. - Vincenzo Librandi, Feb 10 2012

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Feb 10 2012

Mathematica

LinearRecurrence[{2, -1}, {339, 677}, 50] (* Vincenzo Librandi, Feb 10 2012 *)
338*Range[50]+1 (* Harvey P. Dale, Feb 18 2012 *)

Prog

(Magma) I:=[339, 677]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Feb 10 2012
(PARI) for(n=1, 50, print1(338*n + 1", ")); \\ Vincenzo Librandi, Feb 10 2012

Crossrefs

Cf. A173275.

Sequence in context: A186043 A107546 A235880 * A252447 A252441 A236896

Adjacent sequences: A157997 A157998 A157999 * A158001 A158002 A158003

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 14 2009

Status

approved