%I #23 Sep 08 2022 08:45:08

%S 1,-2,0,2,2,-6,-2,10,6,-22,-10,42,22,-86,-42,170,86,-342,-170,682,342,

%T -1366,-682,2730,1366,-5462,-2730,10922,5462,-21846,-10922,43690,

%U 21846,-87382,-43690,174762,87382,-349526,-174762,699050,349526,-1398102,-699050,2796202,1398102,-5592406,-2796202

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

%C First differences of A077980.

%H Vincenzo Librandi, <a href="/A078052/b078052.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 (-1,-2,-2)

%F a(n) = (1/3) * ((-3+5*(-1)^n)/2 * (-2)^floor(n/2) + 2*(-1)^n ). - _Ralf Stephan_, Aug 17 2013

%F a(0)=1, a(1)=-2, a(2)=0, a(n)=-a(n-1)-2*a(n-2)-2*a(n-3). - _Harvey P. Dale_, Mar 26 2015

%t CoefficientList[Series[(1 - x) / (1 + x + 2 x^2 + 2 x^3), {x, 0, 50}], x] (* _Vincenzo Librandi_, Aug 17 2013 *)

%t LinearRecurrence[{-1,-2,-2},{1,-2,0},50] (* _Harvey P. Dale_, Mar 26 2015 *)

%o (PARI) a(n)=1/3*((-3+5*(-1)^n)/2*(-2)^floor(n/2)+2*(-1)^n); \\ _Ralf Stephan_, Aug 17 2013

%o (Magma) I:=[1,-2,0]; [n le 3 select I[n] else -Self(n-1)-2*Self(n-2) -2*Self(n-3): n in [1..50]]; // _Vincenzo Librandi_, Aug 17 2013

%K sign,easy

%O 0,2

%A _N. J. A. Sloane_, Nov 17 2002