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A052988 Expansion of (1-x^2)/(1-2x-2x^2+x^3+x^4).

%I A052988 #20 Jul 02 2025 16:01:58
%S A052988 1,2,5,13,33,85,218,560,1438,3693,9484,24356,62549,160633,412524,
%T A052988 1059409,2720684,6987029,17943493,46080951,118341175,303913730,
%U A052988 780485366,2004376066,5147467959,13219288954,33948652394,87184038671
%N A052988 Expansion of (1-x^2)/(1-2x-2x^2+x^3+x^4).
%H A052988 Harvey P. Dale, <a href="/A052988/b052988.txt">Table of n, a(n) for n = 0..1000</a>
%H A052988 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=1062">Encyclopedia of Combinatorial Structures 1062</a>
%H A052988 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-1,-1)
%F A052988 G.f.: -(-1+x^2)/(1-2*x-2*x^2+x^3+x^4)
%F A052988 Recurrence: {a(0)=1, a(1)=2, a(2)=5, a(3)=13, a(n)+a(n+1)-2*a(n+2)-2*a(n+3)+a(n+4)}
%F A052988 Sum(-1/331*(-49-147*_alpha+25*_alpha^2+76*_alpha^3)*_alpha^(-1-n), _alpha=RootOf(1-2*_Z-2*_Z^2+_Z^3+_Z^4))
%p A052988 spec := [S,{S=Sequence(Union(Prod(Union(Sequence(Prod(Z,Z)),Z),Z),Z))},unlabeled ]: seq(combstruct[count ](spec,size=n), n=0..20);
%t A052988 CoefficientList[Series[(1-x^2)/(1-2x-2x^2+x^3+x^4),{x,0,30}],x] (* or *) LinearRecurrence[{2,2,-1,-1},{1,2,5,13},30] (* _Harvey P. Dale_, Sep 21 2016 *)
%K A052988 easy,nonn
%O A052988 0,2
%A A052988 encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E A052988 More terms from _James Sellers_, Jun 05 2000