A016935 a(n) = (6*n + 2)^3.

8, 512, 2744, 8000, 17576, 32768, 54872, 85184, 125000, 175616, 238328, 314432, 405224, 512000, 636056, 778688, 941192, 1124864, 1331000, 1560896, 1815848, 2097152, 2406104, 2744000, 3112136

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

The generating function is 8 times the g.f. of A016779. - R. J. Mathar, May 07 2008

Examples

			a(1) = (6*1 + 2)^3 = 8^3 = 512.
		

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).

Crossrefs

Cf. A002117, A016779, A016911, A016923, A016933, A016959, A016971.

Programs

Magma

[(6*n+2)^3: n in [0..50]]; // Vincenzo Librandi, May 04 2011

Mathematica

(6*Range[0,30]+2)^3 (* or *) LinearRecurrence[{4,-6,4,-1},{8,512,2744,8000},30] (* Harvey P. Dale, Aug 23 2019 *)

Formula

a(n) = 8*A016779(n). - R. J. Mathar, May 07 2008

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

G.f.: 8*(1+60*x+93*x^2+8*x^3)/(-1+x)^4. - Wesley Ivan Hurt, Oct 02 2020