A016971 a(n) = (6*n + 5)^3.
125, 1331, 4913, 12167, 24389, 42875, 68921, 103823, 148877, 205379, 274625, 357911, 456533, 571787, 704969, 857375, 1030301, 1225043, 1442897, 1685159, 1953125, 2248091, 2571353, 2924207, 3307949
Offset: 0
Examples
a(0) = (6*0 + 5)^3 = 5^3 = 125.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Programs
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Magma
[(6*n+5)^3: n in [0..40]]; // Vincenzo Librandi, May 07 2011
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Mathematica
Table[(6*n + 5)^3, {n, 0, 25}] (* Amiram Eldar, Oct 02 2020 *)
Formula
Sum_{n>=0} 1/a(n) = -Pi^3/(36*sqrt(3)) + 91*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
a(n) = (125+831*x+339*x^2+x^3)/(-1+x)^4. - Wesley Ivan Hurt, Oct 02 2020