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A052969 Expansion of (1-x)/(1-x-2x^2+x^4).

%I A052969 #20 Jul 02 2025 16:01:58
%S A052969 1,0,2,2,5,9,17,33,62,119,226,431,821,1564,2980,5677,10816,20606,
%T A052969 39258,74793,142493,271473,517201,985354,1877263,3576498,6813823,
%U A052969 12981465,24731848,47118280,89768153,171023248,325827706,620755922,1182643181
%N A052969 Expansion of (1-x)/(1-x-2x^2+x^4).
%H A052969 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=1041">Encyclopedia of Combinatorial Structures 1041</a>
%H A052969 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,0,-1).
%F A052969 G.f.: -(-1+x)/(1-2*x^2+x^4-x).
%F A052969 Recurrence: {a(0)=1, a(1)=0, a(2)=2, a(3)=2, a(n)-2*a(n+2)-a(n+3)+a(n+4)=0}.
%F A052969 Sum_(1/283*(29*_alpha+28*_alpha^3-76*_alpha^2+55)*_alpha^(-1-n), _alpha=RootOf(1-2*_Z^2+_Z^4-_Z)).
%F A052969 a(n)+a(n-1) = A052535(n). - _R. J. Mathar_, Nov 28 2011
%p A052969 spec := [S,{S=Sequence(Prod(Union(Prod(Union(Sequence(Z),Z),Z),Z),Z))},unlabeled ]: seq(combstruct[count ](spec,size=n), n=0..20);
%t A052969 CoefficientList[Series[(1-x)/(1-x-2x^2+x^4),{x,0,40}],x] (* or *) LinearRecurrence[{1,2,0,-1},{1,0,2,2},40] (* _Harvey P. Dale_, Oct 20 2017 *)
%Y A052969 Cf. A052535.
%K A052969 easy,nonn
%O A052969 0,3
%A A052969 encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E A052969 More terms from _James Sellers_, Jun 05 2000