OFFSET
1,1
COMMENTS
The identity (648*n^2 - 72*n + 1)^2 - (9*n^2 - n)*(216*n - 12)^2 = 1 can be written as A154514(n)^2 - A154516(n)*a(n)^2 = 1 (see also the second comment at A154514). - Vincenzo Librandi, Jan 30 2012
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (2,-1).
FORMULA
From R. J. Mathar, Jul 29 2009: (Start)
a(n) = 12*(18n-1).
O.g.f.: 12*x*(17+x)/(x-1)^2. (End)
a(n) = 2*a(n-1) - a(n-2).
MATHEMATICA
216Range[40]-12 (* Harvey P. Dale, Feb 01 2011 *)
LinearRecurrence[{2, -1}, {204, 420}, 50] (* Vincenzo Librandi, Jan 30 2012 *)
PROG
(PARI) a(n)=216*n-12 \\ Charles R Greathouse IV, Dec 27 2011
(Magma) I:=[204, 420]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Jan 30 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Jan 11 2009
STATUS
approved