%I
%S 1,2,4,6,9,13,21,36,63,114,211,394,743,1413,2699,5176,9965,19237,
%T 37221,72178,140223,272843,531675,1037408,2026537,3962996,7757437,
%U 15198402,29801165,58478791,114833209,225641444,443643111,872758866,1717846987
%N Number of binary strings of length n with equal numbers of 000 and 101 substrings.
%H R. H. Hardin, <a href="/A164140/b164140.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
