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A118425 Number of binary sequences of length n containing exactly one subsequence 001. 2
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; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

With an additional 0 at the beginning, the convolution of A000071 with itself. Column 1 of A118424.

LINKS

Table of n, a(n) for n=0..33.

FORMULA

G.f.=z^3/(1-2z+z^3)^2.

EXAMPLE

a(4)=4 because we have 0010, 0011, 0001 and 1001.

MAPLE

g:=z^3/(1-2*z+z^3)^2: gser:=series(g, z=0, 40): seq(coeff(gser, z, n), n=0..38);

CROSSREFS

Cf. A000071, A118424.

Sequence in context: A051172 A032192 A212587 * A097809 A272144 A036389

Adjacent sequences:  A118422 A118423 A118424 * A118426 A118427 A118428

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Apr 27 2006

STATUS

approved

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Last modified November 19 16:10 EST 2017. Contains 294936 sequences.