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 A154515(n)^2 - a(n)*A154519(n)^2 = 1 (see also the second comment at A154515). - Vincenzo Librandi, Jan 31 2012
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*(-10 - 8*x)/(x-1)^3. - Vincenzo Librandi, Jan 31 2012
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jan 31 2012
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {10, 38, 84}, 50] (* Vincenzo Librandi, Jan 31 2012 *)
PROG
(PARI) a(n)=9*n^2+n \\ Charles R Greathouse IV, Dec 27 2011
(Magma) I:=[10, 38, 84]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Jan 31 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Jan 11 2009
STATUS
approved