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Number of binary strings of length n with equal numbers of 0000 and 0110 substrings
1

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

%S 1,2,4,8,14,25,44,81,147,271,494,914,1686,3144,5853,10982,20614,38943,

%T 73668,140052,266722,510012,977110,1878151,3616930,6984113,13509815,

%U 26190433,50854110,98922756,192696246,375925007,734270150,1435989377

%N Number of binary strings of length n with equal numbers of 0000 and 0110 substrings

%H R. H. Hardin, <a href="/A164151/b164151.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