A016923 a(n) = (6*n + 1)^3.

1, 343, 2197, 6859, 15625, 29791, 50653, 79507, 117649, 166375, 226981, 300763, 389017, 493039, 614125, 753571, 912673, 1092727, 1295029, 1520875, 1771561, 2048383, 2352637, 2685619, 3048625, 3442951, 3869893, 4330747, 4826809, 5359375, 5929741, 6539203, 7189057

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 1.6.3.

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, A016921.

Programs

Magma

[(6*n+1)^3: n in [0..60]]; // Vincenzo Librandi, May 04 2011

Mathematica

a[n_]:=(6*n + 1)^3; Array[a, 60, 0] (* or *)
LinearRecurrence[{4, -6, 4, -1}, {1, 343, 2197, 6859}, 60] (* or *)
CoefficientList[Series[(1 + 339 x + 831 x^2 + 125 x^3)/(-1 + x)^4, {x, 0, 60}], x] (* Stefano Spezia, Sep 03 2018 *)

Formula

Sum_{n>=0} 1/a(n) = Pi^3/(36*sqrt(3)) + 91*zeta(3)/216.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Wesley Ivan Hurt, Dec 28 2023

From Stefano Spezia, Nov 01 2024: (Start)

E.g.f.: exp(x)*(1 + 342*x + 756*x^2 + 216*x^3).

a(n) = A000578(A016921(n)). (End)