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%I #9 Oct 20 2014 17:14:57
%S 1,2,4,6,10,16,28,46,82,142,256,460,846,1556,2912,5454,10332,19618,
%T 37506,71894,138432,267136,517142,1002904,1949366,3794686,7399060,
%U 14444992,28236426,55251992,108224818,212167258,416284478,817369732
%N a[n] = number of bit strings of length n which have exactly as many substrings 000 as substrings 111.
%D This was motivated by problem 11424 in the 2009 March issue of the American Mathematical monthly.
%H R. H. Hardin, <a href="/A158422/b158422.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.
%K nonn
%O 0,2
%A Dan Jurca (dan.jurca(AT)csueastbay.edu), Mar 18 2009
%E a(11)-a(500)from _R. H. Hardin_, Aug 10 2009
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