%I #18 Sep 08 2022 08:44:41
%S 0,64,512,1728,4096,8000,13824,21952,32768,46656,64000,85184,110592,
%T 140608,175616,216000,262144,314432,373248,438976,512000,592704,
%U 681472,778688,884736,1000000,1124864,1259712,1404928,1560896,1728000,1906624,2097152
%N (4n)^3.
%C Volume of a cube with side 4n. - _Wesley Ivan Hurt_, Jul 05 2014
%H Vincenzo Librandi, <a href="/A016803/b016803.txt">Table of n, a(n) for n = 0..1000</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.: 64*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) = 64 * A000578(n). - _Wesley Ivan Hurt_, Jul 05 2014
%p A016803:=n->64*n^3: seq(A016803(n), n=0..40); # _Wesley Ivan Hurt_, Jul 05 2014
%t Table[64 n^3, {n, 0, 40}] (* or *) CoefficientList[Series[64 x (1 + 4 x + x^2)/(1 - x)^4, {x, 0, 40}], x] (* _Vincenzo Librandi_, Jul 05 2014 *)
%o (Magma) [64*n^3: n in [0..40]] /* or */ I:=[0,64,512,1728]; [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. similar sequences listed in A244725.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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