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%I #9 Oct 20 2014 17:14:58
%S 1,2,4,8,14,24,42,75,138,255,476,894,1690,3217,6149,11805,22732,43897,
%T 84977,164835,320346,623556,1215518,2372496,4636086,9068943,17757267,
%U 34799853,68254019,133968219,263132327,517158572,1017024736,2001152416
%N Number of binary strings of length n with equal numbers of 0001 and 0110 substrings
%H R. H. Hardin, <a href="/A164159/b164159.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