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%I #9 Oct 20 2014 17:14:58
%S 1,2,4,8,14,25,44,77,137,245,442,802,1467,2701,5007,9337,17514,33025,
%T 62580,119107,227609,436522,839915,1620774,3135715,6080701,11815887,
%U 23002577,44853764,87590551,171271524,335292477,657085575,1288945073
%N Number of binary strings of length n with equal numbers of 0000 and 1001 substrings
%H R. H. Hardin, <a href="/A164153/b164153.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