|
%I #19 Jan 27 2022 23:02:23
%S 1,0,2,2,5,9,17,33,62,119,226,431,821,1564,2980,5677,10816,20606,
%T 39258,74793,142493,271473,517201,985354,1877263,3576498,6813823,
%U 12981465,24731848,47118280,89768153,171023248,325827706,620755922,1182643181
%N Expansion of (1-x)/(1-x-2x^2+x^4).
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=1041">Encyclopedia of Combinatorial Structures 1041</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,0,-1).
%F G.f.: -(-1+x)/(1-2*x^2+x^4-x).
%F 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 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 a(n)+a(n-1) = A052535(n). - _R. J. Mathar_, Nov 28 2011
%p 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 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 Cf. A052535.
%K easy,nonn
%O 0,3
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E More terms from _James A. Sellers_, Jun 05 2000
|
