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Number of binary strings of length n with equal numbers of 0000 and 1111 substrings
1

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

%S 1,2,4,8,14,26,48,88,164,302,562,1044,1946,3632,6796,12738,23932,

%T 45044,84976,160610,304222,577358,1097974,2092018,3993784,7638400,

%U 14635854,28092662,54015016,104027610,200667008,387672364,750053450,1453209256

%N Number of binary strings of length n with equal numbers of 0000 and 1111 substrings

%H R. H. Hardin, <a href="/A164154/b164154.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