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
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 14 2009
STATUS
approved