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A163715
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Number of n X 3 binary arrays with all 1s connected, a path of 1s from top row to bottom row, and no 1 having more than two 1s adjacent.
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3
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6, 21, 48, 108, 236, 506, 1080, 2294, 4854, 10248, 21614, 45564, 96028, 202354, 426376, 898374, 1892838, 3988096, 8402638, 17703724, 37300364, 78588906, 165580536, 348864886, 735030230, 1548649464, 3262879566, 6874624124
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OFFSET
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1,1
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COMMENTS
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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) + 2*a(n-3) + a(n-4) - 2*a(n-5) + a(n-6) for n>=10.
Empirical g.f.: x*(1 + x)*(6 - 9*x + 3*x^2 + 6*x^3 - 10*x^4 + 7*x^5 + x^6 - 2*x^7) / ((1 - x)^2*(1 - 2*x - x^4)). - Colin Barker, Feb 22 2018
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EXAMPLE
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All solutions for n=2:
...1.0.0...1.0.0...1.1.0...1.1.0...1.1.1...0.0.1...0.0.1...0.1.1...0.1.1
...1.0.0...1.1.0...1.0.0...1.1.0...1.0.0...0.0.1...0.1.1...0.0.1...0.1.1
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...1.1.1...0.1.0...0.1.0...0.1.0...0.1.1...0.1.1...1.1.0...1.1.0...1.0.0
...0.0.1...0.1.0...0.1.1...1.1.0...0.1.0...1.1.0...0.1.0...0.1.1...1.1.1
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...1.1.1...0.0.1...1.0.1
...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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