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Number of binary strings of length n with equal numbers of 0001 and 0011 substrings
1

%I #9 Oct 20 2014 17:14:58

%S 1,2,4,8,14,26,48,88,166,312,590,1124,2140,4092,7844,15060,28998,

%T 55940,108124,209408,406218,789272,1535792,2992312,5837488,11400876,

%U 22289812,43621496,85444828,167507880,328642084,645245632,1267710158,2492228804

%N Number of binary strings of length n with equal numbers of 0001 and 0011 substrings

%H R. H. Hardin, <a href="/A164156/b164156.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