OFFSET
0,2
COMMENTS
Volume of a cube with side 6*n. - Wesley Ivan Hurt, Jul 05 2014
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
G.f.: 216*x*(1 + 4*x + x^2)/(1 - x)^4. - Vincenzo Librandi, Jul 05 2014
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>3. - Vincenzo Librandi, Jul 05 2014
a(n) = 216 * A000578(n). - Wesley Ivan Hurt, Jul 05 2014
Sum_{n>=1} 1/a(n) = zeta(3)/216. - Amiram Eldar, Oct 02 2020
EXAMPLE
a(1) = (6*1)^3 = 216.
MAPLE
MATHEMATICA
Table[216 n^3, {n, 0, 40}] (* or *) CoefficientList[Series[216 x (1 + 4 x + x^2)/(1 - x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Jul 05 2014 *)
PROG
(Magma) [(6*n)^3: n in [0..40]]; // Vincenzo Librandi, May 03 2011
(Magma) I:=[0, 216, 1728, 5832]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Jul 05 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved