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%I #18 Oct 18 2019 14:48:20
%S 1,2,6,18,52,154,452,1330,3912,11506,33844,99546,292800,861226,
%T 2533164,7450914,21915720,64461730,189604292,557691946,1640365328,
%U 4824883034,14191653468,41742572146,122779374040,361136698450,1062228212084
%N Expansion of (1-x)(1+x)/(1-2*x-3*x^2+2*x^4).
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=1051">Encyclopedia of Combinatorial Structures 1051</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (2,3,0,-2)
%F G.f.: -(-1+x^2)/(1-3*x^2+2*x^4-2*x)
%F Recurrence: {a(0)=1, a(1)=2, a(2)=6, a(3)=18, 2*a(n)-3*a(n+2)-2*a(n+3)+a(n+4)=0}
%F Sum(-1/22*(-3-7*_alpha+4*_alpha^3)*_alpha^(-1-n), _alpha=RootOf(1-3*_Z^2+2*_Z^4-2*_Z))
%p spec := [S,{S=Sequence(Prod(Union(Sequence(Prod(Z,Z)),Z),Union(Z,Z)))},unlabeled ]: seq(combstruct[count ](spec,size=n), n=0..20);
%t CoefficientList[Series[(1-x)(1+x)/(1-2x-3x^2+2x^4),{x,0,30}],x] (* or *) LinearRecurrence[{2,3,0,-2},{1,2,6,18},30] (* _Harvey P. Dale_, Oct 18 2019 *)
%K easy,nonn
%O 0,2
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E More terms from _James A. Sellers_, Jun 06 2000