A017115 a(n) = (8*n + 4)^3.

64, 1728, 8000, 21952, 46656, 85184, 140608, 216000, 314432, 438976, 592704, 778688, 1000000, 1259712, 1560896, 1906624, 2299968, 2744000, 3241792, 3796416, 4410944, 5088448, 5832000, 6644672, 7529536, 8489664, 9528128, 10648000, 11852352, 13144256, 14526784, 16003008

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A002117, A016755, A016827, A017113.

Programs

Magma

[(8*n+4)^3: n in [0..35] ]; // Vincenzo Librandi, Jul 21 2011

Mathematica

LinearRecurrence[{4, -6, 4, -1},{64, 1728, 8000, 21952},24] (* Ray Chandler, Aug 04 2015 *)

Formula

G.f.: 64*(1+x)*(x^2 + 22*x + 1)/(x-1)^4. - R. J. Mathar, Jul 14 2016

From Amiram Eldar, Apr 25 2023: (Start)

a(n) = A017113(n)^3.

a(n) = 2^3*A016827(n) = 2^6*A016755(n).

Sum_{n>=0} 1/a(n) = 7*zeta(3)/512.

Sum_{n>=0} (-1)^n/a(n) = Pi^3/2048. (End)

E.g.f.: 64*exp(x)*(1 + 26*x + 36*x^2 + 8*x^3). - Stefano Spezia, May 27 2025