|
%I #28 Sep 08 2022 08:44:41
%S 64,1000,4096,10648,21952,39304,64000,97336,140608,195112,262144,
%T 343000,438976,551368,681472,830584,1000000,1191016,1404928,1643032,
%U 1906624,2197000,2515456,2863288,3241792
%N a(n) = (6*n + 4)^3.
%H Vincenzo Librandi, <a href="/A016959/b016959.txt">Table of n, a(n) for n = 0..3000</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.: 8*(x^3 + 60*x^2 + 93*x + 8)/(1-x)^4. - _Vincenzo Librandi_, Jan 27 2013
%F Sum_{n>=0} 1/a(n) = -Pi^3 / (324*sqrt(3)) + 13*zeta(3)/216. - _Amiram Eldar_, Oct 02 2020
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - _Wesley Ivan Hurt_, Oct 02 2020
%e a(0) = (6*0 + 4)^3 = 4^3 = 64.
%t CoefficientList[Series[8*(x^3 + 60*x^2 + 93*x + 8)/(1 - x)^4, {x, 0, 40}], x] (* _Vincenzo Librandi_, Jan 27 2013 *)
%t (6*Range[0,30]+4)^3 (* or *) LinearRecurrence[{4,-6,4,-1},{64,1000,4096,10648},30] (* _Harvey P. Dale_, Nov 22 2018 *)
%o (Magma) [(6*n+4)^3: n in [0..40]]; // _Vincenzo Librandi_, May 06 2011
%Y Cf. A002117, A016911, A016923, A016935, A016947, A016971.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
|
