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

0,1

Comments

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

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).

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

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A082385 A236077 A061460 * A241756 A236220 A128794

Adjacent sequences: A016932 A016933 A016934 * A016936 A016937 A016938

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved