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Number of binary strings of length n with equal numbers of 0001 and 0100 substrings
1

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

%S 1,2,4,8,14,24,44,83,156,292,552,1052,2012,3853,7400,14255,27528,

%T 53255,103212,200379,389648,758750,1479400,2887960,5643900,11040973,

%U 21619292,42369251,83101488,163113411,320383832,629695622,1238372630,2436774903

%N Number of binary strings of length n with equal numbers of 0001 and 0100 substrings

%H R. H. Hardin, <a href="/A164157/b164157.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