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A209231 Number of binary words of length n such that there is at least one 0 and every run of consecutive 0's is of length >= 4. 1

%I #15 Jan 15 2013 17:18:32

%S 0,0,0,0,1,3,6,10,15,22,33,51,80,125,193,295,449,684,1045,1600,2451,

%T 3752,5738,8770,13403,20488,31326,47903,73251,112003,171244,261812,

%U 400284,612008,935736,1430709,2187495,3344566,5113646,7818463,11953990

%N Number of binary words of length n such that there is at least one 0 and every run of consecutive 0's is of length >= 4.

%F O.g.f.: x^4/((1-x)*(1-2*x+x^2-x^5)), see Mathematica code for unsimplified form.

%e a(5) = 3 because we have: {0,0,0,0,0}, {0,0,0,0,1}, {1,0,0,0,0}.

%t nn=40; a=x^4/(1-x); CoefficientList[Series[(a+1)/((1-a x/(1-x)))*1/(1-x)-1/(1-x), {x,0,nn}], x]

%Y Cf. A000225, A077855, A130578.

%K nonn

%O 0,6

%A _Geoffrey Critzer_, Jan 12 2013

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