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A164142 Number of binary strings of length n with equal numbers of 001 and 011 substrings 1


%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*(1-2n)*a(n-1) +4(n-1)*a(n-2) +2(2n-3)*a(n-3) +12(2-n)*a(n-4) +4(2n-5)*a(n-5)=0. - R. J. Mathar, Nov 28 2011

%K nonn

%O 0,2

%A _R. H. Hardin_ Aug 11 2009

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Last modified December 8 01:25 EST 2021. Contains 349590 sequences. (Running on oeis4.)