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Expansion of (1-x^3)/(1-x-x^2-x^3+x^5).
0

%I #17 Apr 18 2017 07:04:20

%S 1,1,2,3,6,10,18,32,57,101,180,320,569,1012,1800,3201,5693,10125,

%T 18007,32025,56956,101295,180151,320395,569816,1013406,1802322,

%U 3205393,5700726,10138625,18031338,32068367,57032937,101431916,180394595

%N Expansion of (1-x^3)/(1-x-x^2-x^3+x^5).

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=1044">Encyclopedia of Combinatorial Structures 1044</a>

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

%F G.f.: -(-1+x^3)/(1-x^3-x-x^2+x^5)

%F Recurrence: {a(1)=1, a(0)=1, a(3)=3, a(2)=2, a(4)=6, a(n)-a(n+2)-a(n+3)-a(n+4)+a(n+5)=0}

%F Sum(-1/7031*(-1007-901*_alpha^2-1879*_alpha+1187*_alpha^4-95*_alpha^3)*_alpha^(-1-n), _alpha=RootOf(1-_Z^3-_Z-_Z^2+_Z^5))

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

%t CoefficientList[Series[(1-x^3)/(1-x-x^2-x^3+x^5),{x,0,50}],x] (* or *) LinearRecurrence[{1,1,1,0,-1},{1,1,2,3,6},50] (* _Harvey P. Dale_, Sep 18 2016 *)

%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