A158310 361n + 1.

362, 723, 1084, 1445, 1806, 2167, 2528, 2889, 3250, 3611, 3972, 4333, 4694, 5055, 5416, 5777, 6138, 6499, 6860, 7221, 7582, 7943, 8304, 8665, 9026, 9387, 9748, 10109, 10470, 10831, 11192, 11553, 11914, 12275, 12636, 12997, 13358, 13719, 14080

Offset

1,1

Comments

The identity (361*n+1)^2-(361*n^2+2*n)*(19)^2=1 can be written as a(n)^2-A158309(n)*(19)^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*(19^2*t+2)).

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

Formula

G.f.: x*(362-x)/(1-x)^2.

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

Mathematica

LinearRecurrence[{2, -1}, {362, 723}, 50]
361*Range[40]+1 (* Harvey P. Dale, Jul 09 2016 *)

Prog

(Magma) I:=[362, 723]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 361*n + 1.

Crossrefs

Cf. A158309.

Sequence in context: A013765 A013891 A045098 * A031716 A243131 A155019

Adjacent sequences: A158307 A158308 A158309 * A158311 A158312 A158313

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 16 2009

Status

approved