Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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