%I #12 Sep 08 2022 08:45:32

%S 0,3,3,6,18,24,60,120,216,480,912,1824,3744,7296,14784,29568,58752,

%T 118272,235776,471552,944640,1886208,3775488,7550976,15095808,

%U 30203904,60395520,120791040,241606656,483164160,966377472,1932754944,3865411584,7731019776,15461842944

%N a(n) = 2*a(n-2) + 4*a(n-3), with initial terms 0, 3, 3.

%H Andrew Howroyd, <a href="/A134068/b134068.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,4).

%F From _Andrew Howroyd_, Jan 03 2020: (Start)

%F G.f.: 3*x*(1 + x)/((1 - 2*x)*(1 + 2*x + 2*x^2)).

%F a(n) = 3*A134136(n). (End)

%o (PARI) concat([0], Vec(3*(1 + x)/((1 - 2*x)*(1 + 2*x + 2*x^2)) + O(x^40))) \\ _Andrew Howroyd_, Jan 03 2020

%o (Magma) a:=[0,3,3]; [n le 3 select a[n] else 2*Self(n-2) + 4*Self(n-3):n in [1..35]]; // _Marius A. Burtea_, Jan 03 2020

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 35); [0] cat Coefficients(R!( 3*x*(1 + x)/((1 - 2*x)*(1 + 2*x + 2*x^2)))); // _Marius A. Burtea_, Jan 03 2020

%Y Cf. A134136, A134654.

%K nonn

%O 0,2

%A _Paul Curtz_, Jan 29 2008

%E a(12) corrected and terms a(13) and beyond from _Andrew Howroyd_, Jan 03 2020