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
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).
Programs
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Magma
[3*n^3: n in [0..40]]; // Vincenzo Librandi, Jun 26 2011
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Maple
seq(3*n^3, n=0..38); # Nathaniel Johnston, Jun 26 2011
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Mathematica
3*Range[0, 35]^3 (* Alonso del Arte, Oct 04 2013 *)
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PARI
a(n)=3*n^3 \\ Charles R Greathouse IV, Oct 12 2017
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 = A386403.
Sum_{n>=1} (-1)^(n+1)/a(n) = zeta(3)/4. (End)
Extensions
Edited by N. J. A. Sloane, Apr 30 2006