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%I #13 Jul 06 2016 05:15:57
%S 1,2,4,6,10,19,33,58,110,205,379,723,1383,2630,5056,9770,18846,36485,
%T 70891,137785,268197,523176,1021490,1996255,3906299,7650804,14995686,
%U 29417270,57751714,113448331,223002449,438614490,863149766,1699458781
%N Number of binary strings of length n with equal numbers of 001 and 010 substrings.
%H R. H. Hardin, <a href="/A164141/b164141.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+1)*a(n) +(-4*n-1)*a(n-1) +(8*n-9)*a(n-2) +(-14*n+27)*a(n-3) +(19*n-40)*a(n-4) +2*(-11*n+35)*a(n-5) +4*(5*n-22)*a(n-6) +8*(-n+5)*a(n-7)=0. - _R. J. Mathar_, Dec 10 2013
%K nonn
%O 0,2
%A _R. H. Hardin_, Aug 11 2009
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