A016911 a(n) = (6*n)^3.

0, 216, 1728, 5832, 13824, 27000, 46656, 74088, 110592, 157464, 216000, 287496, 373248, 474552, 592704, 729000, 884736, 1061208, 1259712, 1481544, 1728000, 2000376, 2299968, 2628072, 2985984, 3375000, 3796416, 4251528, 4741632, 5268024, 5832000, 6434856, 7077888

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

From Vincenzo Librandi, Jul 05 2014: (Start)

G.f.: 216*x*(1 + 4*x + x^2)/(1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>3. (End)

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

From Elmo R. Oliveira, Oct 18 2025: (Start)

E.g.f.: 216*x*(1 + 3*x + x^2)*exp(x).

a(n) = A016767(2*n) = A016743(3*n). (End)

Example

a(1) = (6*1)^3 = 216.

Maple

A016911:=n->216*n^3: seq(A016911(n), n=0..40); # Wesley Ivan Hurt, Jul 05 2014

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

Cf. A000578, A002117, A016923, A016935, A016947, A016959, A016971.

Cf. similar sequences listed in A244725.

Cf. A016743, A016767.

Sequence in context: A016863 A033698 A121683 * A370693 A323801 A222694

Adjacent sequences: A016908 A016909 A016910 * A016912 A016913 A016914

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved