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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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1
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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| G.f.: (1-x+x^6)/(1-3*x+2*x^2+x^6-x^7).
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EXAMPLE
| 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
| 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
| 5th column of A145111.
Sequence in context: A059174 A054044 A008859 * A062257 A172316 A062258
Adjacent sequences: A145110 A145111 A145112 * A145114 A145115 A145116
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KEYWORD
| nonn
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AUTHOR
| Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 02 2008
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