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A228791
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Number of n X 3 binary arrays with top left element equal to 1 and no two ones adjacent horizontally or nw-se.
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1
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2, 8, 36, 156, 672, 2892, 12444, 53544, 230388, 991308, 4265376, 18352956, 78968652, 339784392, 1462016004, 6290726844, 27067586208, 116465750508, 501125993916, 2156232718056, 9277785608532, 39920229888492, 171767792616864
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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) = 5*a(n-1) - 3*a(n-2) for n>3.
G.f.: 2*x*(1 - x + x^2) / (1 - 5*x + 3*x^2).
a(n) = -(2^(1-n)*((-11+sqrt(13))*(5+sqrt(13))^n + (5-sqrt(13))^n*(11+sqrt(13)))) / (9*sqrt(13)) for n>1.
(End)
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EXAMPLE
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Some solutions for n=4:
..1..0..0....1..0..0....1..0..0....1..0..1....1..0..1....1..0..1....1..0..1
..1..0..0....0..0..0....0..0..0....0..0..1....0..0..0....0..0..1....1..0..0
..1..0..1....0..0..0....1..0..1....0..1..0....0..1..0....0..0..1....0..0..1
..0..0..1....1..0..0....0..0..1....0..1..0....0..0..0....0..0..0....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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