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A296109
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Number of n X 2 0..1 arrays with each 1 adjacent to 3 or 4 king-move neighboring 1s.
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2
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1, 2, 3, 4, 8, 17, 31, 71, 166, 365, 856, 2020, 4675, 10985, 25869, 60578, 142347, 334748, 785984, 1846905, 4340975, 10198815, 23965446, 56319245, 132336896, 310971516, 730753851, 1717154937, 4035069173, 9481906914, 22281135563
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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Empirical: a(n) = a(n-1) + 2*a(n-2) + 5*a(n-3) - 2*a(n-4) - 6*a(n-5) - 4*a(n-6).
Empirical g.f.: x*(1 + x - x^2 - 8*x^3 - 10*x^4 - 4*x^5) / (1 - x - 2*x^2 - 5*x^3 + 2*x^4 + 6*x^5 + 4*x^6). - Colin Barker, Mar 22 2018
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EXAMPLE
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Some solutions for n=7:
..0..0. .1..1. .0..0. .0..0. .1..1. .0..0. .0..0. .0..0. .1..1. .1..1
..1..1. .1..1. .1..1. .1..1. .1..1. .1..1. .0..0. .1..1. .1..1. .1..1
..1..1. .1..0. .1..1. .1..1. .0..1. .1..1. .0..0. .1..1. .0..1. .1..0
..0..0. .1..0. .1..0. .0..0. .1..1. .1..0. .1..1. .0..0. .0..1. .1..1
..1..1. .1..1. .1..0. .0..0. .0..1. .1..1. .1..1. .0..0. .1..1. .0..1
..1..1. .1..1. .1..1. .1..1. .1..1. .1..1. .0..0. .0..0. .1..1. .1..1
..0..0. .0..0. .1..1. .1..1. .1..1. .0..0. .0..0. .0..0. .0..0. .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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