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%I A163723 #5 Mar 31 2012 12:35:32
%S A163723 1,7,21,49,101,193,351,617,1059,1787,2979,4923,8085,13219,21545,35037,
%T A163723 56889,92269,149539,242229,392231,634967,1027751,1663319,2691721,
%U A163723 4355743,7048221,11404777,18453869,29859577,48314439,78175073,126490635
%N A163723 Number of nX2 binary arrays with all 1s connected, a path of 1s from left column to right column, and no 1 having more than two 1s adjacent
%H A163723 R. H. Hardin, <a href="/A163723/b163723.txt">Table of n, a(n) for n=1..100</a>
%F A163723 Empirical: a(n)=4*a(n-1)-5*a(n-2)+a(n-3)+2*a(n-4)-a(n-5)
%F A163723 Empirical: a(n)=A006355(n+7)-n^2-7n-17. G.f.: x*(1+3*x-2*x^2+x^4-x^3)/((x^2+x-1)*(x-1)^3). [From _R. J. Mathar_, Aug 11 2009]
%e A163723 All solutions for n=3
%e A163723 ...1.1...1.1...1.1...1.1...1.1...0.0...0.0...0.0...0.0...1.0...0.0...0.0...0.1
%e A163723 ...0.0...0.1...1.0...1.1...1.0...0.0...0.1...1.0...1.1...1.0...1.1...1.1...1.1
%e A163723 ...0.0...0.0...0.0...0.0...1.0...1.1...1.1...1.1...1.1...1.1...0.0...0.1...0.0
%e A163723 ------
%e A163723 ...0.0...0.1...1.0...1.0...1.1...1.1...0.1...1.1
%e A163723 ...1.1...1.1...1.1...1.1...0.1...1.0...0.1...0.1
%e A163723 ...1.0...1.0...0.0...0.1...0.1...1.1...1.1...1.1
%K A163723 nonn
%O A163723 1,2
%A A163723 _R. H. Hardin_ Aug 03 2009

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