A119633 a(n) = (A046717(n))^3.

1, 125, 2197, 68921, 1771561, 48627125, 1305751357, 35319837041, 953054410321, 25737699078125, 694870802988517, 18761935323400361, 506568440928284281, 13677382220238009125, 369289011109685057677, 9970806079491650694881, 269211739130501631841441

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..600

Index entries for linear recurrences with constant coefficients, signature (20,210,-540,-729).

Formula

G.f.: x*(1 + 105*x - 513*x^2 - 729*x^3) / ((1 + x)*(1 - 3*x)*(1 + 9*x)*(1 - 27*x)). - R. J. Mathar, Sep 09 2008

a(n) = ((-1)^n + 3^(1+n) + (-1)^n*3^(1+2*n) + 27^n) / 8 for n>0. - Colin Barker, Dec 23 2017

Example

a(3) = 2197 = 13^3 = (A046717(a))^3.

Mathematica

Rest@ Nest[Append[#, 2 #[[-1]] + 3 #[[-2]]] &, {1, 1}, 15]^3 (* or *)
Rest@ CoefficientList[Series[x (1 + 105 x - 513 x^2 - 729 x^3)/((1 + 9 x) (1 - 3 x) (1 - 27 x) (1 + x)), {x, 0, 16}], x] (* Michael De Vlieger, Dec 22 2017 *)

Prog

(PARI) Vec(x*(1 + 105*x - 513*x^2 - 729*x^3) / ((1 + x)*(1 - 3*x)*(1 + 9*x)*(1 - 27*x)) + O(x^40)) \\ Colin Barker, Dec 23 2017

Crossrefs

Cf. A046717, A120096.

Sequence in context: A373007 A080169 A017127 * A017223 A265470 A017331

Adjacent sequences: A119630 A119631 A119632 * A119634 A119635 A119636

Keyword

nonn,easy

Author

Gary W. Adamson, Jun 09 2006

Extensions

Entry revised by N. J. A. Sloane, Aug 11 2019

Status

approved