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a(n) = (A046717(n))^3.
2

%I #27 Aug 11 2019 01:03:10

%S 1,125,2197,68921,1771561,48627125,1305751357,35319837041,

%T 953054410321,25737699078125,694870802988517,18761935323400361,

%U 506568440928284281,13677382220238009125,369289011109685057677,9970806079491650694881,269211739130501631841441

%N a(n) = (A046717(n))^3.

%H Colin Barker, <a href="/A119633/b119633.txt">Table of n, a(n) for n = 1..600</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (20,210,-540,-729).

%F 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

%F a(n) = ((-1)^n + 3^(1+n) + (-1)^n*3^(1+2*n) + 27^n) / 8 for n>0. - _Colin Barker_, Dec 23 2017

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

%t Rest@ Nest[Append[#, 2 #[[-1]] + 3 #[[-2]]] &, {1, 1}, 15]^3 (* or *)

%t 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 *)

%o (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

%Y Cf. A046717, A120096.

%K nonn,easy

%O 1,2

%A _Gary W. Adamson_, Jun 09 2006

%E Entry revised by _N. J. A. Sloane_, Aug 11 2019