A017163 a(n) = (9*n)^3.

0, 729, 5832, 19683, 46656, 91125, 157464, 250047, 373248, 531441, 729000, 970299, 1259712, 1601613, 2000376, 2460375, 2985984, 3581577, 4251528, 5000211, 5832000, 6751269, 7762392, 8869743, 10077696, 11390625, 12812904, 14348907, 16003008, 17779581, 19683000

Offset

0,2

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).

Formula

G.f.: 729*x*(1 + 4*x + x^2)/(x-1)^4. - R. J. Mathar, Jul 17 2014

From Elmo R. Oliveira, Oct 18 2025: (Start)

E.g.f.: 729*x*(1 + 3*x + x^2)*exp(x).

a(n) = 729*A000578(n) = A016767(3*n).

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)

Mathematica

(9*Range[0, 30])^3 (* Harvey P. Dale, Sep 09 2019 *)
(* Alternative: *)
LinearRecurrence[{4, -6, 4, -1}, {0, 729, 5832, 19683}, 30] (* Harvey P. Dale, Sep 09 2019 *)

Prog

(Magma) [(9*n)^3: n in [0..35]]; // Vincenzo Librandi, Jul 22 2011

Crossrefs

Cf. A000578, A016767.

Sequence in context: A219133 A017079 A062556 * A233159 A217969 A017379

Adjacent sequences: A017160 A017161 A017162 * A017164 A017165 A017166

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved