OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
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); a(0)=0, a(1)=81, a(2)=324. - Harvey P. Dale, Nov 06 2012
G.f.: -81*x*(1+x)/(x-1)^3. - R. J. Mathar, Jul 17 2014
From Amiram Eldar, Jan 25 2021: (Start)
Sum_{n>=1} 1/a(n) = Pi^2/486.
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/972.
Product_{n>=1} (1 + 1/a(n)) = sinh(Pi/9)/(Pi/9).
Product_{n>=1} (1 - 1/a(n)) = sin(Pi/9)/(Pi/9). (End)
From Elmo R. Oliveira, Dec 02 2024: (Start)
E.g.f.: 81*exp(x)*x*(1 + x).
MATHEMATICA
(9*Range[0, 30])^2 (* or *) LinearRecurrence[{3, -3, 1}, {0, 81, 324}, 40] (* Harvey P. Dale, Nov 06 2012 *)
PROG
(Magma) [(9*n)^2: n in [0..35]]; // Vincenzo Librandi, Jul 22 2011
(PARI) a(n)=(9*n)^2 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
STATUS
approved