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A118430
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Number of binary sequences of length n containing exactly one subsequence 010.
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10
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0, 0, 0, 1, 4, 10, 22, 47, 98, 199, 396, 777, 1508, 2900, 5534, 10492, 19782, 37119, 69358, 129118, 239578, 443229, 817822, 1505389, 2764986, 5068435, 9273928, 16940488, 30897020, 56271128, 102347564, 185922589, 337353688, 611462514
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OFFSET
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0,5
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COMMENTS
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With only two 0's at the beginning, the convolution of A005314 with itself. Column 1 of A118429.
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LINKS
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FORMULA
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G.f.: z^3/(1-2*z+z^2-z^3)^2.
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EXAMPLE
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a(4) = 4 because we have 0100, 0101, 0010 and 1010.
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MAPLE
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g:=z^3/(1-2*z+z^2-z^3)^2: gser:=series(g, z=0, 40): seq(coeff(gser, z, n), n=0..38);
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MATHEMATICA
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LinearRecurrence[{4, -6, 6, -5, 2, -1}, {0, 0, 0, 1, 4, 10}, 40] (* Jean-François Alcover, May 11 2019 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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