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%I #22 Mar 04 2022 17:07:05
%S 1,1,2,5,9,22,45,101,218,477,1041,2270,4957,10813,23602,51501,112393,
%T 245270,535245,1168053,2549002,5562621,12139137,26490894,57810301,
%U 126157741,275310370,600801805,1311112313,2861202246,6243918445
%N Expansion of (1-2x^2)/(1-x-3x^2+2x^4).
%H Harvey P. Dale, <a href="/A052962/b052962.txt">Table of n, a(n) for n = 0..1000</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=1033">Encyclopedia of Combinatorial Structures 1033</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,0,-2).
%F G.f.: -(-1+2*x^2)/(1-3*x^2+2*x^4-x)
%F Recurrence: {a(1)=1, a(0)=1, a(3)=5, a(2)=2, 2*a(n)-3*a(n+2)-a(n+3)+a(n+4)=0}
%F Sum(-1/397*(-190*_alpha-78*_alpha^2+116*_alpha^3+15)*_alpha^(-1-n), _alpha=RootOf(1-3*_Z^2+2*_Z^4-_Z))
%p spec := [S,{S=Sequence(Prod(Union(Sequence(Prod(Union(Z,Z),Z)),Z),Z))},unlabeled ]: seq(combstruct[count ](spec,size=n), n=0..20);
%t CoefficientList[Series[(1-2x^2)/(1-x-3x^2+2x^4),{x,0,30}],x] (* or *) LinearRecurrence[{1,3,0,-2},{1,1,2,5},40] (* _Harvey P. Dale_, Feb 20 2016 *)
%K easy,nonn
%O 0,3
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E More terms from _James A. Sellers_, May 04 2000
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