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Search: id:A145116
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| A145116 |
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Numbers of length n binary words with fewer than 8 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, 128, 256, 512, 1023, 2043, 4079, 8143, 16255, 32447, 64767, 129279, 258047, 515072, 1028102, 2052126, 4096110, 8175966, 16319486, 32574206, 65019134, 129780222, 259045373, 517062645, 1032073165, 2060050221
(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^9)/(1-3*x+2*x^2+x^9-x^10).
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EXAMPLE
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a(10) = 1023 = 2^10-1, because 1000000001 is the only binary word of length 10 with not less than 8 0-digits between any pair of consecutive 1-digits.
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MAPLE
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a:= n-> (Matrix([[2, 1$9]]). Matrix(10, (i, j)-> if i=j-1 then 1 elif j=1 then [3, -2, 0$6, -1, 1][i] else 0 fi)^n)[1, 2]: seq (a(n), n=0..35);
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CROSSREFS
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8th column of A145111.
Sequence in context: A009714 A051535 A008862 this_sequence A122265 A113010 A056767
Adjacent sequences: A145113 A145114 A145115 this_sequence A145117 A145118 A145119
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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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