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A188819
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Number of n X 3 binary arrays without the pattern 0 1 diagonally or antidiagonally.
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1
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8, 25, 48, 81, 120, 169, 224, 289, 360, 441, 528, 625, 728, 841, 960, 1089, 1224, 1369, 1520, 1681, 1848, 2025, 2208, 2401, 2600, 2809, 3024, 3249, 3480, 3721, 3968, 4225, 4488, 4761, 5040, 5329, 5624, 5929, 6240, 6561, 6888, 7225, 7568, 7921, 8280, 8649
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).
G.f.: x*(8 + 9*x - 2*x^2 + x^3) / ((1 - x)^3*(1 + x)).
a(n) = (2 + 8*n + 8*n^2) / 2 for n even.
a(n) = (8*n + 8*n^2) / 2 for n odd.
(End)
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EXAMPLE
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Some solutions for 4 X 3:
..1..1..1....1..1..1....1..1..0....1..1..1....1..0..1....0..1..0....0..1..0
..0..1..1....1..1..1....1..0..1....1..1..1....0..0..0....1..0..1....1..0..1
..1..0..1....1..0..0....0..1..0....1..1..1....0..0..0....0..0..0....0..1..0
..0..0..0....0..0..0....0..0..1....1..1..1....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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