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A231356
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Number of (n+1) X (1+1) 0..3 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with values 0..3 introduced in row major order.
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1
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1, 2, 4, 12, 33, 102, 329, 1075, 3622, 12298, 42132, 145145, 501380, 1735895, 6017101, 20873202, 72444888, 251507292, 873325097, 3032847106, 10533086197, 36583055791, 127062078054, 441325714766, 1532875934756, 5324239108913
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OFFSET
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1,2
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LINKS
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FORMULA
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Empirical: a(n) = 3*a(n-1) + 5*a(n-2) - 5*a(n-3) - 24*a(n-4) - 2*a(n-5) + 15*a(n-6) + 9*a(n-7).
Empirical g.f.: x*(1 - x - 7*x^2 - 5*x^3 + 11*x^4 + 13*x^5 + 3*x^6) / ((1 - x)*(1 - x - 2*x^2 - x^3)*(1 - x - 6*x^2 - 9*x^3)). - Colin Barker, Sep 28 2018
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EXAMPLE
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Some solutions for n=7:
..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0
..0..1....0..1....0..0....0..0....0..1....0..1....0..1....0..1....0..0....0..1
..1..1....1..1....1..1....0..1....1..1....1..1....1..1....1..1....0..0....1..1
..1..2....2..2....1..1....1..1....1..2....2..2....0..0....1..1....0..0....1..1
..2..2....2..1....1..1....1..2....2..2....2..2....0..0....1..1....0..0....2..2
..3..3....1..1....1..1....2..2....0..0....0..0....0..0....2..2....0..0....2..1
..3..2....1..3....1..1....0..0....0..1....0..0....1..1....2..1....1..1....1..1
..2..2....3..3....1..1....0..0....1..1....0..0....1..1....1..1....1..1....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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