%I
%S 1,2,4,6,10,16,30,56,110,208,396,740,1402,2660,5116,9860,19106,36996,
%T 71788,139332,271040,527936,1030348,2013128,3938218,7710220,15108552,
%U 29627244,58144136,114187880,224405644,441273096,868220258,1709129948
%N Number of binary strings of length n with equal numbers of 001 and 011 substrings
%H R. H. Hardin, <a href="/A164142/b164142.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]
%F Conjecture: n*a(n)+2*(12n)*a(n1) +4(n1)*a(n2) +2(2n3)*a(n3) +12(2n)*a(n4) +4(2n5)*a(n5)=0.  R. J. Mathar, Nov 28 2011
%K nonn
%O 0,2
%A _R. H. Hardin_ Aug 11 2009
