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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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2
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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, 7802519550
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: (1-x+x^8)/(1-3*x+2*x^2+x^8-x^9).
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EXAMPLE
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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
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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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MATHEMATICA
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CoefficientList[Series[(1 - x + x^8) / (1 - 3 x + 2 x^2 + x^8 - x^9), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 06 2013 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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