OFFSET
1,1
COMMENTS
The identity (13122*n^2 - 324*n + 1)^2 - (81*n^2 - 2*n)*(1458*n - 18)^2 = 1 can be written as A157509(n)^2 - A157507(n)*a(n)^2 = 1 (see also second comment at A157509). - 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.: 18*(82*x-1)/(x-1)^2. - Vincenzo Librandi, Jan 26 2012 [corrected by Georg Fischer, May 11 2019]
MATHEMATICA
LinearRecurrence[{2, -1}, {1440, 2898}, 40] (* Vincenzo Librandi, Jan 26 2012 *)
1458*Range[40]-18 (* Harvey P. Dale, Jul 03 2024 *)
PROG
(Magma) I:=[1440, 2898]; [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, 35, print1(1458*n - 18", ")); \\ Vincenzo Librandi, Jan 26 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 02 2009
STATUS
approved