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%I #11 Apr 07 2020 22:25:59
%S 1,2,4,8,14,26,50,100,200,400,800,1600,3200,6400,12800,25600,51200,
%T 102400,204800,409600,819200,1638400,3276800,6553600,13107200,
%U 26214400,52428800,104857600,209715200,419430400,838860800,1677721600,3355443200
%N Number of binary strings of length n with equal numbers of 0001 and 1000 substrings.
%H R. H. Hardin, <a href="/A164161/b164161.txt">Table of n, a(n) for n=0..500</a>
%H Shalosh B. Ekhad and Doron Zeilberger, <a href="http://arxiv.org/abs/1112.6207">Automatic Solution of Richard Stanley's Amer. Math. Monthly Problem #11610 and ANY Problem of That Type</a>, arXiv preprint arXiv:1112.6207, 2011. See subpages for rigorous derivations of g.f., recurrence, asymptotics for this sequence. [From _N. J. A. Sloane_, Apr 07 2012]
%o (Empirical) (bc) (z is number of 0's) z=3; for(i=0; i<=500; i++) { if(i<=z)a=2^i else if(i<=2*z)a=2*a-2 else a=2*a; a }
%K nonn
%O 0,2
%A _R. H. Hardin_, Aug 11 2009
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