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Search: id:A118425
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| A118425 |
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Number of binary sequences of length n containing exactly one subsequence 001. |
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+0
2
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| 0, 0, 0, 1, 4, 12, 30, 68, 144, 291, 568, 1080, 2012, 3688, 6672, 11941, 21180, 37284, 65210, 113420, 196320, 338375, 581040, 994416, 1696824, 2887632, 4902240, 8304073, 14038324, 23688636, 39905238, 67118420, 112726512, 189072363
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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With an additional 0 at the beginning, the convolution of A000071 with itself. Column 1 of A118424.
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FORMULA
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G.f.=z^3/(1-2z+z^3)^2.
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EXAMPLE
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a(4)=4 because we have 0010, 0011, 0001, and 1001.
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MAPLE
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g:=z^3/(1-2*z+z^3)^2: gser:=series(g, z=0, 40): seq(coeff(gser, z, n), n=0..38);
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CROSSREFS
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Cf. A000071, A118424.
Sequence in context: A051172 A011797 A032192 this_sequence A097809 A036389 A036388
Adjacent sequences: A118422 A118423 A118424 this_sequence A118426 A118427 A118428
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 27 2006
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