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Number of binary strings of length n with equal numbers of 0000 and 0010 substrings
1

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

%S 1,2,4,8,14,25,46,86,160,294,545,1016,1904,3565,6686,12585,23770,

%T 45013,85392,162393,309621,591792,1133516,2175532,4184036,8062871,

%U 15566675,30105898,58320830,113156619,219878845,427850213,833616314,1626199001

%N Number of binary strings of length n with equal numbers of 0000 and 0010 substrings

%H R. H. Hardin, <a href="/A164148/b164148.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