OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,-9).
FORMULA
G.f.: -3*(x-1)*x/(3*x-1)^2.
a(n) = 3^(n-1)*(2*n+1) for n>0, a(0) = 0.
a(n) = 3*A081038(n-1) for n>0.
From Amiram Eldar, May 17 2022: (Start)
Sum_{n>=1} 1/a(n) = 3*(sqrt(3)*arctanh(1/sqrt(3)) - 1).
Sum_{n>=1} (-1)^(n+1)/a(n) = 3 - sqrt(3)*Pi/2. (End)
MAPLE
a:= n-> `if`(n=0, 0, 3^(n-1)*(2*n+1)):
seq(a(n), n=0..30);
MATHEMATICA
a[0] = 0; a[n_] := 3^(n - 1)*(2*n + 1); Array[a, 30, 0] (* Amiram Eldar, May 17 2022 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Sep 18 2013
STATUS
approved