A117642 a(n) = 3*n^3.

0, 3, 24, 81, 192, 375, 648, 1029, 1536, 2187, 3000, 3993, 5184, 6591, 8232, 10125, 12288, 14739, 17496, 20577, 24000, 27783, 31944, 36501, 41472, 46875, 52728, 59049, 65856, 73167, 81000, 89373, 98304, 107811, 117912, 128625, 139968, 151959, 164616

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n+1) = a(n) + 9*n^2 + 9*n + 3 with a(0) = 0. - Jean-Bernard François, Oct 04 2013

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Wesley Ivan Hurt, May 27 2021

From Amiram Eldar, Jan 10 2023: (Start)

Sum_{n>=1} 1/a(n) = zeta(3)/3.

Sum_{n>=1} (-1)^(n+1)/a(n) = zeta(3)/4. (End)

a(n) = n*(2*A000217(n) + A000217(2*n-1)). - Charlie Marion, Mar 01 2024

Maple

seq(3*n^3, n=0..38); # Nathaniel Johnston, Jun 26 2011

Mathematica

3*Range[0, 35]^3 (* Alonso del Arte, Oct 04 2013 *)

Prog

(Magma) [3*n^3: n in [0..40]]; // Vincenzo Librandi, Jun 26 2011
(PARI) a(n)=3*n^3 \\ Charles R Greathouse IV, Oct 12 2017

Crossrefs

Cf. A000578, A002117, A033431.

Sequence in context: A347108 A027158 A251781 * A220834 A276243 A211618

Adjacent sequences: A117639 A117640 A117641 * A117643 A117644 A117645

Keyword

nonn,easy

Author

Roger L. Bagula, Apr 10 2006

Extensions

Edited by N. J. A. Sloane, Apr 30 2006

Status

approved