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%I #5 Jul 26 2022 11:57:38
%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.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,-2,4,0,-1).
%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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