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A210100
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Number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock having one or three distinct values, and new values 0..2 introduced in row major order.
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1
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7, 30, 135, 614, 2799, 12766, 58231, 265622, 1211647, 5526990, 25211655, 115004294, 524598159, 2392982206, 10915714711, 49792609142, 227131616287, 1036072863150, 4726101083175, 21558359689574, 98339596281519, 448581262028446
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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) - 7*a(n-2) + 2*a(n-3).
G.f.: x*(7 - 12*x + 4*x^2) / ((1 - x)*(1 - 5*x + 2*x^2)).
a(n) = (1/2) + (2^(-2-n)*((5-sqrt(17))^n*(-11+3*sqrt(17)) + (5+sqrt(17))^n*(11+3*sqrt(17)))) / sqrt(17).
(End)
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EXAMPLE
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Some solutions for n=4:
..0..1....0..1....0..0....0..1....0..1....0..0....0..1....0..1....0..0....0..0
..0..2....2..2....0..0....0..2....1..2....1..2....0..2....2..0....1..2....0..0
..1..2....1..0....0..0....2..1....0..1....0..2....1..1....0..1....2..0....0..0
..2..0....0..2....0..0....0..2....2..2....1..0....1..1....2..2....1..2....0..0
..1..0....2..1....0..0....1..0....1..0....2..1....2..0....2..2....1..0....1..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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