%I #26 Sep 08 2022 08:46:00

%S 2,6,-2,30,14,30,238,-66,782,990,46,8190,-178,16926,48238,-15810,

%T 247694,106590,262318,1932414,-555058,6518430,7830766,765630,67043342,

%U -2865954,143077678,387537150,-124309426,2044005150,807673198,2285861694,15681525902,-4648416930

%N Expansion of -2*x*(1+4*x) / ((2*x-1)*(4*x^2+3*x+1)).

%H Vincenzo Librandi, <a href="/A200563/b200563.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-1,2,8).

%F a(n) = -a(n-1) +2*a(n-2) +8*a(n-3).

%F a(n) = (6*4^n+r^(n+1)+(16/r)^(n+1))/(7*2^n), where r=-3-sqrt(-7). - _Bruno Berselli_, Dec 12 2011

%t LinearRecurrence[{-1,2,8}, {2,6,-2},34] (* _Bruno Berselli_, Dec 12 2011 *)

%o (Maxima) makelist(expand((6*4^n+(-3-sqrt(-7))^(n+1)+(-3+sqrt(-7))^(n+1))/(7*2^n)),n,1,34); /* _Bruno Berselli_, Dec 12 2011 */

%o (Magma) I:=[2, 6, -2]; [n le 3 select I[n] else -Self(n-1)+2*Self(n-2)+8*Self(n-3): n in [1..40]]; // _Vincenzo Librandi_, Jul 12 2012

%K sign,easy

%O 1,1

%A _Krishnamurthy Balasubraniam_, Nov 19 2011

%E Definition from _R. J. Mathar_, Nov 19 2011