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A205220
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Number of (n+1) X 3 0..1 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..1 introduced in row major order.
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1
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20, 52, 132, 340, 868, 2228, 5700, 14612, 37412, 95860, 245508, 628948, 1610980, 4126772, 10570692, 27077780, 69360548, 177671668, 455113860, 1165800532, 2986255972, 7649458100, 19594481988, 50192314388, 128570242340, 329339499892
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OFFSET
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1,1
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COMMENTS
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REFERENCES
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LINKS
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FORMULA
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Empirical: a(n) = a(n-1) +4*a(n-2).
G.f.: 4*x*(5 + 8*x) / (1 - x - 4*x^2).
a(n) = (2^(2-n)*((1-sqrt(17))^n*(-4+sqrt(17)) + (1+sqrt(17))^n*(4+sqrt(17)))) / sqrt(17).
(End)
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EXAMPLE
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Some solutions for n=4:
..0..0..0....0..1..0....0..1..1....0..0..1....0..1..1....0..0..1....0..1..0
..0..0..1....1..1..0....0..0..0....1..0..1....0..1..0....0..0..1....1..1..0
..1..0..1....0..0..0....0..0..1....0..1..1....1..1..0....1..1..1....0..0..1
..0..1..1....1..0..0....1..0..1....0..0..0....1..1..1....1..0..0....1..0..1
..1..1..1....0..1..0....1..0..0....1..1..0....1..0..0....0..1..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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