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A145113
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Numbers of length n binary words with fewer than 5 0-digits between any pair of consecutive 1-digits.
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3
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1, 2, 4, 8, 16, 32, 64, 127, 251, 495, 975, 1919, 3775, 7424, 14598, 28702, 56430, 110942, 218110, 428797, 842997, 1657293, 3258157, 6405373, 12592637, 24756478, 48669960, 95682628, 188107100, 369808828, 727025020, 1429293563, 2809917167, 5524151707
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: (1-x+x^6)/(1-3*x+2*x^2+x^6-x^7).
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EXAMPLE
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a(7) = 127 = 2^7-1, because 1000001 is the only binary word of length 7 with not less than 5 0-digits between any pair of consecutive 1-digits.
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MAPLE
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a:= n-> (Matrix([[2, 1$6]]). Matrix(7, (i, j)-> if i=j-1 then 1 elif j=1 then [3, -2, 0$3, -1, 1][i] else 0 fi)^n)[1, 2]: seq(a(n), n=0..40);
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MATHEMATICA
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CoefficientList[Series[(1 - x + x^6) / (1 - 3 x + 2 x^2 + x^6 - x^7), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 06 2013 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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