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
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 18 2009
STATUS
approved