A158223 a(n) = 196*n + 1.

197, 393, 589, 785, 981, 1177, 1373, 1569, 1765, 1961, 2157, 2353, 2549, 2745, 2941, 3137, 3333, 3529, 3725, 3921, 4117, 4313, 4509, 4705, 4901, 5097, 5293, 5489, 5685, 5881, 6077, 6273, 6469, 6665, 6861, 7057, 7253, 7449, 7645, 7841, 8037, 8233, 8429

Offset

1,1

Comments

The identity (196*n + 1)^2 - (196*n^2 + 2*n)*14^2 = 1 can be written as a(n)^2 - A158222(n)*14^2 = 1.

Also, the identity (392*n + 1)^2 - (196*n^2 + n)*28^2 = 1 can be written as A158002(n)^2 - (n*a(n))*28^2 = 1. - Vincenzo Librandi, Feb 23 2012

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 (first identity in the comment section: row 15 in the initial table at p. 85, case d(t) = t*(14^2*t+2); second identity: row 14, case d(t) = t*(14^2*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*(197-x)/(1-x)^2.

Mathematica

LinearRecurrence[{2, -1}, {197, 393}, 50]
196 Range[50]+1 (* Harvey P. Dale, Jul 23 2021 *)

Prog

(Magma) I:=[197, 393]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 196*n + 1.

Crossrefs

Cf. A158222, A158002.

Sequence in context: A142274 A142624 A294187 * A142503 A142568 A188336

Adjacent sequences: A158220 A158221 A158222 * A158224 A158225 A158226

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 14 2009

Status

approved