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A209231
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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.
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1
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0, 0, 0, 0, 1, 3, 6, 10, 15, 22, 33, 51, 80, 125, 193, 295, 449, 684, 1045, 1600, 2451, 3752, 5738, 8770, 13403, 20488, 31326, 47903, 73251, 112003, 171244, 261812, 400284, 612008, 935736, 1430709, 2187495, 3344566, 5113646, 7818463, 11953990
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OFFSET
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0,6
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LINKS
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FORMULA
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O.g.f.: x^4/((1-x)*(1-2*x+x^2-x^5)), see Mathematica code for unsimplified form.
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EXAMPLE
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a(5) = 3 because we have: {0,0,0,0,0}, {0,0,0,0,1}, {1,0,0,0,0}.
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MATHEMATICA
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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]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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