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%I #21 Apr 18 2017 07:04:20
%S 1,1,4,10,27,73,196,528,1421,3825,10296,27714,74599,200801,540504,
%T 1454896,3916201,10541393,28374684,76377258,205587683,553388489,
%U 1489577660,4009555040,10792677717,29051077025,78197931824,210488462658,566580111247,1525086070785
%N Expansion of ( 1-x ) / ( 1-2*x-2*x^2+x^4 ).
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=1055">Encyclopedia of Combinatorial Structures 1055</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,0,-1).
%F G.f.: (1-x)/(1-2*x-2*x^2+x^4).
%F Recurrence: {a(1)=1, a(0)=1, a(2)=4, a(3)=10, a(n)-2*a(n+2)-2*a(n+3)+a(n+4)=0}.
%F Sum(-1/182*(-35*_alpha+2*_alpha^3+22*_alpha^2-25)*_alpha^(-1-n), _alpha=RootOf(1-2*_Z-2*_Z^2+_Z^4)).
%p spec := [S,{S=Sequence(Prod(Union(Prod(Z,Z),Z),Union(Sequence(Z),Z)))},unlabeled ]: seq(combstruct[count ](spec,size=n), n=0..20);
%t CoefficientList[Series[(1 - x)/(1 - 2*x - 2*x^2 + x^4), {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Nov 13 2014 *)
%t LinearRecurrence[{2,2,0,-1},{1,1,4,10},30] (* _Harvey P. Dale_, Oct 03 2016 *)
%K easy,nonn
%O 0,3
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E More terms from _James A. Sellers_, Jun 06 2000
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