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A118425 Number of binary sequences of length n containing exactly one subsequence 001. 2

%I

%S 0,0,0,1,4,12,30,68,144,291,568,1080,2012,3688,6672,11941,21180,37284,

%T 65210,113420,196320,338375,581040,994416,1696824,2887632,4902240,

%U 8304073,14038324,23688636,39905238,67118420,112726512,189072363

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

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

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

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

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

%Y Cf. A000071, A118424.

%K nonn

%O 0,5

%A _Emeric Deutsch_, Apr 27 2006

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Last modified April 20 08:32 EDT 2019. Contains 322306 sequences. (Running on oeis4.)