OFFSET
1,2
COMMENTS
Limit_{n->infinity} a(n)/a(n-1) = 649 + 180*sqrt(13).
This sequence gives the values of y in solutions of the Diophantine equation x^2 - 13*y^2 = 1. The corresponding x values are in A114047. - Vincenzo Librandi, Aug 08 2010, edited by Jon E. Schoenfield, May 04 2014
LINKS
Colin Barker, Table of n, a(n) for n = 1..322
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (1298,-1).
FORMULA
a(n) = 1298*a(n-1) - a(n-2), n>1. - Michael Somos, Oct 30 2002
a(n) = ((649 + 180*sqrt(13))^n - (649 - 180*sqrt(13))^n) / (2*sqrt(13)).
From Mohamed Bouhamida, Sep 20 2006: (Start)
a(n) = 1297*(a(n-1) + a(n-2)) - a(n-3).
a(n) = 1299*(a(n-1) - a(n-2)) + a(n-3). (End)
G.f.: 180*x^2/(1-1298*x+x^2). - Philippe Deléham, Nov 18 2008
MATHEMATICA
LinearRecurrence[{1298, -1}, {0, 180}, 50] (* Vincenzo Librandi, Jun 14 2015 *)
PROG
(PARI) concat(0, Vec(180*x^2/(1-1298*x+x^2) + O(x^20))) \\ Colin Barker, Jun 13 2015
(Magma) I:=[0, 180]; [n le 2 select I[n] else 1298*Self(n-1)-Self(n-2): n in [1..20]]; // Vincenzo Librandi, Jun 14 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gregory V. Richardson, Oct 16 2002
STATUS
approved