OFFSET
1,1
COMMENTS
The identity (388962*n^2 - 1764*n + 1)^2 - (441*n^2 - 2*n)*(18522*n - 42)^2 = 1 can be written as a(n)^2 - A157737(n)*A157738(n)^2 = 1. - Vincenzo Librandi, Jan 25 2012
This is the case s=21 of the identity (2*s^4*n^2 - 4*s^2*n + 1)^2 - (s^2*n^2 - 2*n)*(2*s^3*n - 2*s)^2 = 1. - Bruno Berselli, Feb 05 2011
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
G.f.: x*(-387199 - 390724*x - x^2)/(x-1)^3. - Vincenzo Librandi, Jan 25 2012
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jan 25 2012
a(n) = 2*A158319(n)^2 - 1. - Bruno Berselli, Feb 05 2012
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {387199, 1552321, 3495367}, 40] (* Vincenzo Librandi, Jan 25 2012 *)
PROG
(Magma) I:=[387199, 1552321, 3495367]; [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 25 2012
(PARI) for(n=1, 22, print1(388962*n^2-1764*n+1", ")); \\ Vincenzo Librandi, Jan 25 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 05 2009
STATUS
approved