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A209724
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1/4 the number of (n+1) X 6 0..2 arrays with every 2 X 2 subblock having distinct clockwise edge differences.
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3
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8, 9, 10, 12, 14, 18, 22, 30, 38, 54, 70, 102, 134, 198, 262, 390, 518, 774, 1030, 1542, 2054, 3078, 4102, 6150, 8198, 12294, 16390, 24582, 32774, 49158, 65542, 98310, 131078, 196614, 262150, 393222, 524294, 786438, 1048582, 1572870, 2097158
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OFFSET
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1,1
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COMMENTS
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Conjecture: a(1) = 8; for n > 1, a(n) is the smallest integer m such that m = ((2x * a(n-1)) /(x+1)) - x , with x a positive nontrivial divisor of m. (This is true at least for a(1) to a(100).) - Enric Reverter i Bigas, Oct 11 2020
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LINKS
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FORMULA
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Empirical: a(n) = a(n-1) +2*a(n-2) -2*a(n-3).
G.f.: x*(8 + x - 15*x^2) / ((1 - x)*(1 - 2*x^2)).
a(n) = 3*2^(n/2-1) + 6 for n even.
a(n) = 2^((n+1)/2) + 6 for n odd.
(End)
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EXAMPLE
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Some solutions for n=4:
..2..1..2..1..2..1....2..0..2..0..1..0....2..1..2..1..2..1....0..1..0..1..0..2
..0..2..0..2..0..2....1..2..1..2..0..2....0..2..0..2..0..2....2..0..2..0..2..1
..1..0..1..0..1..0....2..0..2..0..1..0....2..1..2..1..2..1....0..1..0..1..0..2
..0..2..0..2..0..2....1..2..1..2..0..2....0..2..0..2..0..2....2..0..2..0..2..1
..1..0..1..0..1..0....2..0..2..0..1..0....1..0..1..0..1..0....0..1..0..1..0..2
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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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