A157956 a(n) = 200*n + 1.

201, 401, 601, 801, 1001, 1201, 1401, 1601, 1801, 2001, 2201, 2401, 2601, 2801, 3001, 3201, 3401, 3601, 3801, 4001, 4201, 4401, 4601, 4801, 5001, 5201, 5401, 5601, 5801, 6001, 6201, 6401, 6601, 6801, 7001, 7201, 7401, 7601, 7801, 8001, 8201, 8401, 8601

Offset: 1

Author

Vincenzo Librandi, Mar 10 2009

Keywords

• nonn
• easy

Comments

The identity (200*n + 1)^2 - (100*n^2 + n)*20^2 = 1 can be written as a(n)^2 - A055438(n)*20^2 = 1. - Vincenzo Librandi, Feb 04 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 (row 14 in the first table at p. 85, case d(t) = t*(10^2*t+1)).
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A055438.

Programs

Magma

I:=[201, 401]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Feb 04 2012

Mathematica

200Range[50]+1  (* Harvey P. Dale, Feb 24 2011 *)
LinearRecurrence[{2, -1}, {201, 401}, 50] (* Vincenzo Librandi, Feb 04 2012 *)

PARI

for(n=1, 50, print1(200*n + 1", ")); \\ Vincenzo Librandi, Feb 04 2012

Formula

G.f.: x*(201-x)/(1-x)^2. - Vincenzo Librandi, Feb 04 2012

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Feb 04 2012