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 - a(n)* A157508(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 (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*(-79 - 83*x)/(x-1)^3. - Vincenzo Librandi, Jan 26 2012
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {79, 320, 723}, 40] (* Vincenzo Librandi, Jan 26 2012 *)
Table[81n^2-2n, {n, 40}] (* Harvey P. Dale, Jun 10 2020 *)
PROG
(Magma) I:=[79, 320, 723]; [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(81*n^2 - 2*n", ")); \\ Vincenzo Librandi, Jan 26 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 02 2009
STATUS
approved