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%I #25 Apr 18 2017 07:04:20
%S 1,0,1,3,5,14,34,81,200,487,1187,2899,7072,17256,42109,102748,250717,
%T 611779,1492805,3642610,8888370,21688597,52922564,129136875,315108171,
%U 768898587,1876197092,4578127192,11171133721,27258794552,66514455833
%N Expansion of (1 - 2x)/(1 - 2x - x^2 - x^3 + 2x^4).
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=1046">Encyclopedia of Combinatorial Structures 1046</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,1,-2)
%F G.f.: -(-1+2*x)/(1-2*x-x^3+2*x^4-x^2).
%F Recurrence: {a(1)=0, a(0)=1, a(2)=1, a(3)=3, 2*a(n)-a(n+1)-a(n+2)-2*a(n+3)+a(n+4)=0}
%F Sum(1/4999*(-159+1343*_alpha-450*_alpha^2+136*_alpha^3)*_alpha^(-1-n), _alpha=RootOf(1-2*_Z-_Z^3+2*_Z^4-_Z^2))
%p spec := [S,{S=Sequence(Prod(Union(Sequence(Union(Z,Z)),Z),Z,Z))},unlabeled ]: seq(combstruct[count ](spec,size=n), n=0..20);
%t CoefficientList[Series[(1 - 2 x)/(1 - 2 x - x^2 - x^3 + 2 x^4), {x, 0, 40}], x] (* _Wesley Ivan Hurt_, Jan 15 2017 *)
%K easy,nonn
%O 0,4
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E More terms from _James A. Sellers_, Jun 06 2000
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