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Search: id:A145113
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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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+0
2
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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
(list; graph; listen)
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OFFSET
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0,2
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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..35);
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CROSSREFS
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5th column of A145111.
Sequence in context: A059174 A054044 A008859 this_sequence A062257 A062258 A066178
Adjacent sequences: A145110 A145111 A145112 this_sequence A145114 A145115 A145116
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 02 2008
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