A158402 a(n) = 841*n - 1.

840, 1681, 2522, 3363, 4204, 5045, 5886, 6727, 7568, 8409, 9250, 10091, 10932, 11773, 12614, 13455, 14296, 15137, 15978, 16819, 17660, 18501, 19342, 20183, 21024, 21865, 22706, 23547, 24388, 25229, 26070, 26911, 27752, 28593, 29434

Offset

1,1

Comments

The identity (841*n-1)^2 - (841*n^2-2*n)*(29)^2 = 1 can be written as a(n)^2 - A158401(n)*(29)^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*(29^2*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*(840+x)/(1-x)^2.

Mathematica

LinearRecurrence[{2, -1}, {840, 1681}, 50]
841 Range[40]-1  (* Harvey P. Dale, Jan 29 2011 *)

Prog

(Magma) I:=[840, 1681]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 841*n - 1.

Crossrefs

Cf. A158401.

Sequence in context: A179670 A092002 A169827 * A361421 A045477 A232099

Adjacent sequences: A158399 A158400 A158401 * A158403 A158404 A158405

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 18 2009

Status

approved