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A145117
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Numbers of length n binary words with fewer than 9 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, 128, 256, 512, 1024, 2047, 4091, 8175, 16335, 32639, 65215, 130303, 260351, 520191, 1039359, 2076672, 4149254, 8290334, 16564334, 33096030, 66126846, 132123390, 263986430, 527452670, 1053865982, 2105655293
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| G.f.: (1-x+x^10)/(1-3*x+2*x^2+x^10-x^11).
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EXAMPLE
| a(11) = 2047 = 2^11-1, because 10000000001 is the only binary word of length 11 with not less than 9 0-digits between any pair of consecutive 1-digits.
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MAPLE
| a:= n-> (Matrix([[2, 1$10]]). Matrix(11, (i, j)-> if i=j-1 then 1 elif j=1 then [3, -2, 0$7, -1, 1][i] else 0 fi)^n)[1, 2]: seq (a(n), n=0..35);
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CROSSREFS
| 9th column of A145111.
Sequence in context: A113010 A056767 A008863 * A172320 A168082 A168083
Adjacent sequences: A145114 A145115 A145116 * A145118 A145119 A145120
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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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