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 A157516(n)^2 - A157514(n)*a(n)^2 = 1 (see also the second part of the comment at A157514). - Vincenzo Librandi, Jan 26 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
a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jan 26 2012
G.f.: x*(980 + 20*x)/(1-x)^2. - Vincenzo Librandi, Jan 26 2012
MATHEMATICA
LinearRecurrence[{2, -1}, {980, 1980}, 50] (* Vincenzo Librandi, Jan 26 2012 *)
1000*Range[40]-20 (* or *) Range[980, 40000, 1000](* Harvey P. Dale, Jul 03 2024 *)
PROG
(Magma) I:=[980, 1980]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Jan 26 2012
(PARI) for(n=1, 22, print1(1000*n - 20", ")); \\ Vincenzo Librandi, Jan 26 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 02 2009
STATUS
approved