OFFSET
1,1
COMMENTS
The identity (2048*n^2 - 128*n + 1)^2 - (16*n^2 - n)*(512*n - 16)^2 = 1 can be written as A157448(n)^2 - A157446(n)*a(n)^2 = 1 (see also second comment at A157446). - 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*(16*x + 496)/(x-1)^2. - Vincenzo Librandi, Jan 26 2012
MATHEMATICA
LinearRecurrence[{2, -1}, {496, 1008}, 40] (* Vincenzo Librandi, Jan 26 2012 *)
512*Range[50]-16 (* Harvey P. Dale, Apr 09 2019 *)
PROG
(Magma) I:=[496, 1008]; [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(512*n - 16", ")); \\ Vincenzo Librandi, Jan 26 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 01 2009
STATUS
approved