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

Author

Emeric Deutsch, Apr 27 2006

Keywords

• nonn

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A000071, A118424.

Programs

Maple

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

Formula

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