A118425 Number of binary sequences of length n containing exactly one subsequence 001.

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

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.

Index entries for linear recurrences with constant coefficients, signature (4,-4,-2,4,0,-1).

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: A032192 A212587 A338223 * A097809 A272144 A036389

Adjacent sequences: A118422 A118423 A118424 * A118426 A118427 A118428

Keyword

nonn

Author

Emeric Deutsch, Apr 27 2006

Status

approved