A016959 a(n) = (6*n + 4)^3.

64, 1000, 4096, 10648, 21952, 39304, 64000, 97336, 140608, 195112, 262144, 343000, 438976, 551368, 681472, 830584, 1000000, 1191016, 1404928, 1643032, 1906624, 2197000, 2515456, 2863288, 3241792

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..3000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

G.f.: 8*(x^3 + 60*x^2 + 93*x + 8)/(1-x)^4. - Vincenzo Librandi, Jan 27 2013

Sum_{n>=0} 1/a(n) = -Pi^3 / (324*sqrt(3)) + 13*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

Example

a(0) = (6*0 + 4)^3 = 4^3 = 64.

Mathematica

CoefficientList[Series[8*(x^3 + 60*x^2 + 93*x + 8)/(1 - x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Jan 27 2013 *)
(6*Range[0, 30]+4)^3 (* or *) LinearRecurrence[{4, -6, 4, -1}, {64, 1000, 4096, 10648}, 30] (* Harvey P. Dale, Nov 22 2018 *)

Prog

(Magma) [(6*n+4)^3: n in [0..40]]; // Vincenzo Librandi, May 06 2011

Crossrefs

Cf. A002117, A016911, A016923, A016935, A016947, A016971.

Sequence in context: A220678 A224162 A224413 * A224392 A224025 A270272

Adjacent sequences: A016956 A016957 A016958 * A016960 A016961 A016962

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved