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A163723
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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
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1
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1, 7, 21, 49, 101, 193, 351, 617, 1059, 1787, 2979, 4923, 8085, 13219, 21545, 35037, 56889, 92269, 149539, 242229, 392231, 634967, 1027751, 1663319, 2691721, 4355743, 7048221, 11404777, 18453869, 29859577, 48314439, 78175073, 126490635
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OFFSET
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1,2
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LINKS
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FORMULA
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Empirical: a(n)=4*a(n-1)-5*a(n-2)+a(n-3)+2*a(n-4)-a(n-5)
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]
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EXAMPLE
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All solutions for n=3
...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
...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
...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
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...0.0...0.1...1.0...1.0...1.1...1.1...0.1...1.1
...1.1...1.1...1.1...1.1...0.1...1.0...0.1...0.1
...1.0...1.0...0.0...0.1...0.1...1.1...1.1...1.1
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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