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%I #23 Jul 25 2021 03:45:48
%S 1,2,4,8,17,36,76,161,341,722,1529,3238,6857,14521,30751,65121,137906,
%T 292042,618454,1309693,2773522,5873456,12438151,26340131,55780196,
%U 118125087,250152154,529744373,1121833637,2375694341,5030980901
%N Expansion of (1-x^3)/(1-2x-x^3+x^4).
%C Partial sums of A052908. - _R. J. Mathar_, Nov 28 2011
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=881">Encyclopedia of Combinatorial Structures 881</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,1,-1)
%F G.f.: -(-1+x^3)/(1-2*x-x^3+x^4)
%F Recurrence: {a(0)=1, a(2)=4, a(1)=2, a(3)=8, a(n)-a(n+1)-2*a(n+3)+a(n+4)=0}
%F Sum(-1/643*(-222-40*_alpha-93*_alpha^2+54*_alpha^3)*_alpha^(-1-n), _alpha=RootOf(1-2*_Z-_Z^3+_Z^4))
%F a(n) = A052908(n)-A052908(n-3), n>3. - _R. J. Mathar_, Apr 26 2017
%p spec := [S,{S=Sequence(Union(Z,Prod(Sequence(Prod(Z,Z,Z)),Z)))},unlabeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t CoefficientList[Series[(1-x^3)/(1-2x-x^3+x^4),{x,0,40}],x] (* or *) LinearRecurrence[{2,0,1,-1},{1,2,4,8},40] (* _Harvey P. Dale_, Jul 21 2021 *)
%K easy,nonn
%O 0,2
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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