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%I #11 Oct 20 2014 17:14:57
%S 1,2,4,6,8,11,18,36,76,153,289,525,954,1787,3464,6832,13452,26207,
%T 50603,97525,188805,367994,720805,1414179,2772486,5428759,10626469,
%U 20818945,40850896,80275617,157897960,310707852,611510788,1203795095,2370700373
%N Number of binary strings of length n with equal numbers of 001 and 101 substrings
%C Seems to obey an 8-term hypergeometric recurrence with cubic polynomial coefficients. - R. J. Mathar, Nov 28 2011.
%H R. H. Hardin, <a href="/A164144/b164144.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]
%K nonn
%O 0,2
%A _R. H. Hardin_ Aug 11 2009
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