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A296798
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Number of n X 2 0..1 arrays with each 1 adjacent to 1, 3 or 4 king-move neighboring 1s.
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1
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2, 8, 15, 41, 122, 308, 855, 2405, 6522, 18080, 50223, 138353, 383114, 1061116, 2933431, 8119437, 22473514, 62177224, 172075759, 476212281, 1317772378, 3646788996, 10092010711, 27927735285, 77286019354, 213877500592
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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) = a(n-1) + 3*a(n-2) + 9*a(n-3) - 4*a(n-4) - 12*a(n-5) - 16*a(n-6).
Empirical g.f.: x*(1 + 2*x)*(2 + 2*x - 3*x^2 - 10*x^3 - 8*x^4) / ((1 - x^2 - 2*x^3)*(1 - x - 2*x^2 - 8*x^3)). - Colin Barker, Feb 25 2019
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EXAMPLE
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Some solutions for n=7:
..1..1. .1..0. .1..0. .0..0. .1..1. .0..0. .0..1. .1..0. .0..0. .0..0
..0..0. .1..0. .0..1. .1..0. .1..1. .0..0. .1..0. .1..0. .1..1. .1..0
..1..1. .0..0. .0..0. .0..1. .0..0. .1..0. .0..0. .1..1. .0..0. .0..1
..1..1. .1..1. .1..1. .1..1. .1..1. .0..1. .1..0. .1..1. .1..0. .0..0
..0..1. .1..1. .0..0. .1..1. .0..0. .0..0. .1..0. .0..0. .0..1. .0..0
..0..1. .0..1. .0..1. .0..1. .0..1. .0..1. .0..0. .1..0. .1..1. .0..1
..0..0. .0..1. .0..1. .0..1. .1..0. .0..1. .0..0. .1..0. .1..1. .0..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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