%I #9 Oct 20 2014 17:14:58
%S 1,2,4,8,14,24,40,67,114,200,364,684,1316,2565,5025,9843,19232,37464,
%T 72808,141327,274332,533044,1037436,2022982,3952284,7734625,15157799,
%U 29737631,58389819,114721663,225516727,443516486,872626728,1717649820
%N Number of binary strings of length n with equal numbers of 0001 and 1001 substrings
%H R. H. Hardin, <a href="/A164162/b164162.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