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A205329
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Number of (n+1) X 3 0..2 arrays with the number of equal 2 X 2 subblock diagonal pairs and equal antidiagonal pairs differing from each horizontal or vertical neighbor, and new values 0..2 introduced in row major order.
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1
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72, 594, 4860, 39852, 326592, 2676888, 21939984, 179823888, 1473863040, 12080008224, 99009584064, 811497652416, 6651158427648, 54513908309376, 446804301553920, 3662076158892288, 30014934381324288, 246006977148006912
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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) = 6*a(n-1) + 18*a(n-2).
G.f.: 18*x*(4 + 9*x) / (1 - 6*x - 18*x^2). - Colin Barker, Jun 11 2018
a(n) = ((9-5*sqrt(3))*(3-3*sqrt(3))^n + (3*(1+sqrt(3)))^n*(9+5*sqrt(3))) / 2.
(End)
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EXAMPLE
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Some solutions for n=4:
..0..0..0....0..1..1....0..0..0....0..0..1....0..1..1....0..0..0....0..1..1
..0..1..2....1..1..1....1..1..0....2..1..2....2..2..1....0..0..1....0..2..1
..0..1..1....0..2..1....0..1..0....1..0..0....1..2..0....2..0..1....2..2..0
..0..0..2....1..0..0....2..2..1....2..2..0....2..1..2....2..0..0....0..0..1
..2..2..1....1..2..0....0..2..0....1..2..1....1..1..2....2..2..2....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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