|
%I #30 Sep 08 2022 08:44:41
%S 0,216,1728,5832,13824,27000,46656,74088,110592,157464,216000,287496,
%T 373248,474552,592704,729000,884736,1061208,1259712,1481544,1728000,
%U 2000376,2299968,2628072,2985984,3375000,3796416,4251528,4741632,5268024,5832000
%N a(n) = (6*n)^3.
%C Volume of a cube with side 6*n. - _Wesley Ivan Hurt_, Jul 05 2014
%H Vincenzo Librandi, <a href="/A016911/b016911.txt">Table of n, a(n) for n = 0..2000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F G.f.: 216*x*(1 + 4*x + x^2)/(1 - x)^4. - _Vincenzo Librandi_, Jul 05 2014
%F 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
%F a(n) = 216 * A000578(n). - _Wesley Ivan Hurt_, Jul 05 2014
%F Sum_{n>=1} 1/a(n) = zeta(3)/216. - _Amiram Eldar_, Oct 02 2020
%e a(1) = (6*1)^3 = 216.
%p A016911:=n->216*n^3: seq(A016911(n), n=0..40); # _Wesley Ivan Hurt_, Jul 05 2014
%t 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 *)
%o (Magma) [(6*n)^3: n in [0..40]]; // _Vincenzo Librandi_, May 03 2011
%o (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
%Y Cf. A000578, A002117, A016923, A016935, A016947, A016959, A016971.
%Y Cf. similar sequences listed in A244725.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
|
