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 A052989 Expansion of ( 1-x ) / ( 1-x-x^2-x^4+x^5 ). 0

%I

%S 1,0,1,1,3,3,7,10,19,29,52,84,145,239,407,678,1146,1918,3232,5421,

%T 9121,15314,25749,43252,72701,122146,205282,344931,579662,974038,

%U 1636836,2750523,4622090,7766989,13051877,21932553,36855997,61933449,104074334

%N Expansion of ( 1-x ) / ( 1-x-x^2-x^4+x^5 ).

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=1063">Encyclopedia of Combinatorial Structures 1063</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,1,-1).

%F G.f.: -(-1+x)/(1-x-x^2-x^4+x^5)

%F Recurrence: {a(1)=0, a(0)=1, a(2)=1, a(3)=1, a(4)=3, a(n)-a(n+1)-a(n+3)-a(n+4)+a(n+5) =0}

%F Sum(-1/8519*(-389-2111*_alpha+619*_alpha^2-358*_alpha^3+541*_alpha^4)*_alpha^(-1-n), _alpha=RootOf(1-_Z-_Z^2-_Z^4+_Z^5))

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

%t CoefficientList[Series[(1-x)/(1-x-x^2-x^4+x^5),{x,0,40}],x] (* or *) LinearRecurrence[{1,1,0,1,-1},{1,0,1,1,3},40] (* _Harvey P. Dale_, Sep 01 2017 *)

%K easy,nonn

%O 0,5

%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000

%E More terms from _James A. Sellers_, Jun 06 2000

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Last modified May 25 11:27 EDT 2020. Contains 334592 sequences. (Running on oeis4.)