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 a(n)^2 - A157446(n)*A157447(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 (3,-3,1).
FORMULA
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jan 26 2012
G.f.: x*(-1921 - 2174*x - x^2)/(x-1)^3. - Vincenzo Librandi, Jan 26 2012
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {1921, 7937, 18049}, 40] (* Vincenzo Librandi, Jan 26 2012 *)
PROG
(Magma) I:=[1921, 7937, 18049]; [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, Jan 26 2012
(PARI) for(n=1, 22, print1(2048*n^2 - 128*n + 1", ")); \\ Vincenzo Librandi, Jan 26 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 01 2009
STATUS
approved