A016959 a(n) = (6*n + 4)^3.

64, 1000, 4096, 10648, 21952, 39304, 64000, 97336, 140608, 195112, 262144, 343000, 438976, 551368, 681472, 830584, 1000000, 1191016, 1404928, 1643032, 1906624, 2197000, 2515456, 2863288, 3241792

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Examples

			a(0) = (6*0 + 4)^3 = 4^3 = 64.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..3000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A002117, A016911, A016923, A016935, A016947, A016971.

Programs

Magma

[(6*n+4)^3: n in [0..40]]; // Vincenzo Librandi, May 06 2011

Mathematica

CoefficientList[Series[8*(x^3 + 60*x^2 + 93*x + 8)/(1 - x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Jan 27 2013 *)
(6*Range[0,30]+4)^3 (* or *) LinearRecurrence[{4,-6,4,-1},{64,1000,4096,10648},30] (* Harvey P. Dale, Nov 22 2018 *)

Formula

G.f.: 8*(x^3 + 60*x^2 + 93*x + 8)/(1-x)^4. - Vincenzo Librandi, Jan 27 2013

Sum_{n>=0} 1/a(n) = -Pi^3 / (324*sqrt(3)) + 13*zeta(3)/216. - Amiram Eldar, Oct 02 2020

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Wesley Ivan Hurt, Oct 02 2020