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Expansion of (1-x)/(1-3x-4x^2+4x^3).
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%I #17 Apr 18 2017 07:04:19

%S 1,2,10,34,134,498,1894,7138,26998,101970,385350,1455938,5501334,

%T 20786354,78540646,296762018,1121303222,4236795154,16008550278,

%U 60487618562,228549876182,863565901682,3262946735526,12328904308578

%N Expansion of (1-x)/(1-3x-4x^2+4x^3).

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=1036">Encyclopedia of Combinatorial Structures 1036</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (3,4,-4)

%F G.f.: -(-1+x)/(1-3*x-4*x^2+4*x^3)

%F Recurrence: {a(0)=1, a(1)=2, a(2)=10, 4*a(n)-4*a(n+1)-3*a(n+2)+a(n+3)=0}

%F Sum(-1/158*(-17-49*_alpha+40*_alpha^2)*_alpha^(-1-n), _alpha=RootOf(1-3*_Z-4*_Z^2+4*_Z^3))

%p spec := [S,{S=Sequence(Prod(Union(Z,Z,Sequence(Z)),Union(Z,Z)))},unlabeled ]: seq(combstruct[count ](spec,size=n), n=0..20);

%t CoefficientList[Series[(1-x)/(1-3x-4x^2+4x^3),{x,0,40}],x] (* or *) LinearRecurrence[{3,4,-4},{1,2,10},40] (* _Harvey P. Dale_, Dec 01 2016 *)

%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