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A268735
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Number of n X 3 binary arrays with some 1 horizontally or vertically adjacent to some other 1 exactly once.
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1
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2, 15, 80, 396, 1788, 7831, 33170, 137868, 563486, 2275119, 9091772, 36031648, 141793168, 554669335, 2158604934, 8363066408, 32273565050, 124112115647, 475807505288, 1819019281732, 6936664653476, 26392068734023, 100206016839642
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OFFSET
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1,1
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LINKS
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FORMULA
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Empirical: a(n) = 4*a(n-1) + 8*a(n-2) - 24*a(n-3) - 38*a(n-4) + 4*a(n-5) + 12*a(n-6) - a(n-8).
Empirical g.f.: x*(2 + 7*x + 4*x^2 + 4*x^3 - 7*x^5 + 2*x^6) / (1 - 2*x - 6*x^2 + x^4)^2. - Colin Barker, Jan 14 2019
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EXAMPLE
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Some solutions for n=4:
..1..0..0. .1..0..1. .0..0..1. .1..0..0. .0..0..1. .1..0..0. .1..0..0
..1..0..0. .0..0..0. .0..0..1. .1..0..1. .0..0..1. .1..0..0. .1..0..0
..0..0..0. .1..1..0. .0..1..0. .0..0..0. .0..0..0. .0..1..0. .0..0..1
..0..0..1. .0..0..1. .0..0..0. .0..0..0. .1..0..1. .1..0..0. .1..0..0
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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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