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A163686
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Number of n X 3 binary arrays with all 1s connected, a path of 1s from upper left corner to lower right corner, and no 1 having more than two 1s adjacent.
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1
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1, 5, 17, 39, 83, 175, 375, 807, 1732, 3690, 7805, 16441, 34605, 72893, 153653, 323917, 682654, 1438292, 3030059, 6383675, 13449863, 28338555, 59708355, 125801331, 265051912, 558439806, 1176585241, 2478972461, 5223002977, 11004454185
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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) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 2*a(n-4) - 6*a(n-5) + 6*a(n-6) - 2*a(n-7) - a(n-8) + a(n-9) for n>=13.
Empirical g.f.: x*(1 + 2*x^2 - 6*x^3 + 10*x^4 - 4*x^5 - 2*x^6 + 4*x^7 + 6*x^8 + 2*x^9 - 3*x^10 - 2*x^11) / ((1 - x)^2*(1 - x + x^2 + x^3)*(1 - 2*x - x^4)). - Colin Barker, Mar 25 2018
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EXAMPLE
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All solutions for n=3:
...1.0.0...1.0.0...1.0.0...1.0.0...1.1.0...1.1.0...1.1.1...1.1.1...1.1.0
...1.1.0...1.1.1...1.0.0...1.0.1...1.0.0...1.0.1...1.0.0...1.0.1...0.1.0
...0.1.1...0.0.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...0.1.1
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...1.1.0...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.0.1...1.1.1
...0.1.1...0.0.1...0.0.1...1.0.1...1.0.1...1.0.1...1.0.1...0.0.1
...0.0.1...0.0.1...0.1.1...0.0.1...0.1.1...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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