OFFSET
1,1
COMMENTS
The identity (5000*n^2 + 200*n + 1)^2 - (25*n^2 + n)*(1000*n + 20)^2 = 1 can be written as a(n)^2 - A173089(n)*A157510(n)^2 = 1 (see also second part of the comment at A173089). - Vincenzo Librandi, Feb 04 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 (3,-3,1).
FORMULA
From Harvey P. Dale, May 24 2011: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(1)=5201, a(2)=20401, a(3)=45601.
G.f.: -x*((5201 + x*(4798+x))/(x-1)^3). (End)
MATHEMATICA
Table[5000n^2+200n+1, {n, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {5201, 20401, 45601}, 40] (* Harvey P. Dale, May 24 2011 *)
PROG
(Magma) I:=[5201, 20401, 45601]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 04 2012
(PARI) for(n=1, 40, print1(5000*n^2 + 200*n + 1", ")); \\ Vincenzo Librandi, Feb 04 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 02 2009
STATUS
approved