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%I #9 Oct 20 2014 17:14:57
%S 1,2,4,6,9,17,31,50,87,167,302,528,992,1907,3518,6539,12645,24327,
%T 46006,88361,172240,332882,641385,1249453,2441841,4748632,9252605,
%U 18128340,35506424,69433187,136116163,267424477,525052400,1030970356,2027883854
%N Number of binary strings of length n with equal numbers of 000 and 010 substrings
%H R. H. Hardin, <a href="/A164138/b164138.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