A017091 a(n) = (8*n + 2)^3.

8, 1000, 5832, 17576, 39304, 74088, 125000, 195112, 287496, 405224, 551368, 729000, 941192, 1191016, 1481544, 1815848, 2197000, 2628072, 3112136, 3652264, 4251528, 4913000, 5639752, 6434856, 7301384, 8242408, 9261000, 10360232, 11543176, 12812904, 14172488, 15625000

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, A016815, A017089 (8n+2), A000578 (n^3).

Programs

Magma

[(8*n+2)^3: n in [0..35]]; // Vincenzo Librandi, Jul 12 2011

Mathematica

(8*Range[0,30]+2)^3 (* or *) LinearRecurrence[{4,-6,4,-1},{8,1000,5832,17576},30] (* Harvey P. Dale, Dec 30 2019 *)

Formula

G.f.: 8*(1 + 121*x + 235*x^2 + 27*x^3)/(x-1)^4. - R. J. Mathar, Jul 14 2016

From Amiram Eldar, Apr 24 2023: (Start)

a(n) = A017089(n)^3.

a(n) = 2^3*A016815(n).

Sum_{n>=0} 1/a(n) = Pi^3/512 + 7*zeta(3)/128. (End)