OFFSET
0,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
Sum_{n>=0} 1/a(n) = 7*zeta(3)/216. - Amiram Eldar, Oct 02 2020
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Wesley Ivan Hurt, Oct 02 2020
G.f.: 27*(1+x)*(1+22*x+x^2)/(-1+x)^4. - Wesley Ivan Hurt, Oct 02 2020
From Amiram Eldar, Mar 30 2022: (Start)
a(n) = A016945(n)^3.
a(n) = 3^3*A016755(n).
Sum_{n>=0} (-1)^n/a(n) = Pi^3/864. (End)
EXAMPLE
a(0) = (6*0 + 3)^3 = 3^3 = 27.
MATHEMATICA
Table[(6*n + 3)^3, {n, 0, 25}] (* Amiram Eldar, Oct 02 2020 *)
PROG
(Magma) [(6*n+3)^3: n in [0..50]]; // Vincenzo Librandi, May 05 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved