A016947 a(n) = (6*n + 3)^3.

27, 729, 3375, 9261, 19683, 35937, 59319, 91125, 132651, 185193, 250047, 328509, 421875, 531441, 658503, 804357, 970299, 1157625, 1367631, 1601613, 1860867, 2146689, 2460375, 2803221, 3176523, 3581577, 4019679, 4492125, 5000211, 5545233, 6128487, 6751269

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Examples

			a(0) = (6*0 + 3)^3 = 3^3 = 27.
		

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. A000578, A002117, A016755, A016911, A016923, A016935, A016945, A016946, A016959, A016971.

Programs

Magma

[(6*n+3)^3: n in [0..50]]; // Vincenzo Librandi, May 05 2011

Mathematica

Table[(6*n + 3)^3, {n, 0, 25}] (* Amiram Eldar, Oct 02 2020 *)
LinearRecurrence[{4,-6,4,-1},{27,729,3375,9261},40] (* Harvey P. Dale, Jul 02 2025 *)

Formula

Sum_{n>=0} 1/a(n) = 7*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.: 27*(1+x)*(1+22*x+x^2)/(-1+x)^4. - Wesley Ivan Hurt, Oct 02 2020

From Amiram Eldar, Mar 30 2022: (Start)

a(n) = A016945(n)^3.

a(n) = 3^3*A016755(n).

Sum_{n>=0} (-1)^n/a(n) = Pi^3/864. (End)