%I #20 Sep 08 2022 08:45:08

%S 1,1,2,1,1,-2,-3,-7,-6,-7,1,6,21,25,34,17,1,-50,-83,-135,-118,-87,65,

%T 214,453,537,562,193,-319,-1250,-1955,-2567,-2022,-679,2433,5798,9589,

%U 10521,8514,-143,-12671,-29842,-42227,-46727,-29270,8457,72641,139638,195365,189721,105810,-95199,-368831

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

%C Row sums of Riordan array (1/(1-x^2), x*(1-2*x^2)/(1-x^2)), A117355. - _Paul Barry_, Mar 09 2006

%H Harvey P. Dale, <a href="/A077948/b077948.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, 1, -2).

%F a(n) = Sum_{k=0..n} Sum_{j=0..n-k} C(j-(n-k)/2-1,j)*C(k,j)*(1+(-1)^(n-k))/2. - _Paul Barry_, Mar 09 2006

%F a(n) = a(n-1) + a(n-2) - 2*a(n-3). If defined by this recurrence, the sequence could be preceded by 0, 0. - _Paul Curtz_, Feb 17 2008

%t CoefficientList[Series[1/(1-x-x^2+2x^3),{x,0,60}],x] (* or *) LinearRecurrence[{1,1,-2},{1,1,2},60] (* _Harvey P. Dale_, Mar 15 2013 *)

%o (PARI) Vec(1/(1-x-x^2+2*x^3)+O(x^60)) \\ _Charles R Greathouse IV_, Sep 25 2012

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( 1/(1-x-x^2+2*x^3) )); // _G. C. Greubel_, Jul 03 2019

%o (Sage) (1/(1-x-x^2+2*x^3)).series(x, 60).coefficients(x, sparse=False) # _G. C. Greubel_, Jul 03 2019

%o (GAP) a:=[1,1,2];; for n in [4..60] do a[n]:= a[n-1]+a[n-2]-2*a[n-3]; od; a; # _G. C. Greubel_, Jul 03 2019

%Y Cf. A077971.

%K sign,easy

%O 0,3

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