%I #9 Oct 20 2014 17:14:58
%S 1,2,4,8,14,24,43,76,134,244,449,828,1551,2934,5564,10620,20390,39236,
%T 75721,146612,284397,552594,1075770,2097260,4093515,7999814,15650618,
%U 30646304,60063574,117815288,231263619,454266068,892880558,1756030324
%N Number of binary strings of length n with equal numbers of 0001 and 0101 substrings
%H R. H. Hardin, <a href="/A164158/b164158.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