OFFSET
1,1
COMMENTS
The identity (103680000*n^2 - 28800*n + 1)^2 - (3600*n^2 - n)*(1728000*n - 240)^2 = 1 can be written as A157859(n)^2 - A157857(n)*a(n)^2 = 1. - Vincenzo Librandi, Jan 25 2012
This is the case s=60 of the identity (8*n^2*s^4 - 8*n*s^2 + 1)^2 - (n^2*s^2 - n)*(8*n*s^3 - 4*s)^2 = 1. - Bruno Berselli, Jan 25 2012
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Vincenzo Librandi, X^2-AY^2=1
Index entries for linear recurrences with constant coefficients, signature (2,-1).
FORMULA
G.f.: x*(1727760 + 240*x)/(1-x)^2. - Colin Barker, Jan 17 2012
a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jan 25 2012
MATHEMATICA
LinearRecurrence[{2, -1}, {1727760, 3455760}, 40] (* Vincenzo Librandi, Jan 25 2012 *)
PROG
(Magma) I:=[1727760, 3455760]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..40]]; // Vincenzo Librandi, Jan 25 2012
(PARI) for(n=1, 22, print1(1728000*n - 240", ")); \\ Vincenzo Librandi, Jan 25 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 08 2009
STATUS
approved