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A145115
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Numbers of length n binary words with fewer than 7 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, 511, 1019, 2031, 4047, 8063, 16063, 31999, 63743, 126976, 252934, 503838, 1003630, 1999198, 3982334, 7932670, 15801598, 31476221, 62699509, 124895181, 248786733, 495574269, 987166205, 1966399741, 3916997885
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| G.f.: (1-x+x^8)/(1-3*x+2*x^2+x^8-x^9).
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EXAMPLE
| a(9) = 511 = 2^9-1, because 100000001 is the only binary word of length 9 with not less than 7 0-digits between any pair of consecutive 1-digits.
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MAPLE
| a:= n-> (Matrix([[2, 1$8]]). Matrix(9, (i, j)-> if i=j-1 then 1 elif j=1 then [3, -2, 0$5, -1, 1][i] else 0 fi)^n)[1, 2]: seq (a(n), n=0..35);
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CROSSREFS
| 7th column of A145111.
Sequence in context: A097000 A054046 A008861 * A172318 A104144 A194632
Adjacent sequences: A145112 A145113 A145114 * A145116 A145117 A145118
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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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