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A198638
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Number of 2n X 2 0..2 arrays with values 0..2 introduced in row major order and each element equal to an even number of horizontal and vertical neighbors.
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1
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4, 36, 376, 3936, 41216, 431616, 4519936, 47333376, 495681536, 5190844416, 54359228416, 569257230336, 5961339109376, 62427953627136, 653754017775616, 6846200955273216, 71694347178868736, 750792950862053376
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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) = 12*a(n-1) -16*a(n-2) for n>3.
G.f.: 4*x*(1 - x)*(1 - 2*x) / (1 - 12*x + 16*x^2).
a(n) = ((6 - 2*sqrt(5))^n*(-5+3*sqrt(5)) + (2*(3+sqrt(5)))^n*(5+3*sqrt(5))) / (16*sqrt(5)) for n>1.
(End)
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EXAMPLE
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Some solutions for n=3:
..0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1
..1..0....1..2....1..0....1..2....2..0....2..0....1..0....2..0....1..2....2..0
..0..2....2..0....2..1....0..1....0..1....0..1....2..1....1..2....0..1....1..2
..2..0....0..2....0..2....2..2....1..2....1..2....1..2....2..1....1..2....0..1
..1..1....2..0....2..0....2..2....2..0....2..1....0..1....0..2....2..1....1..0
..1..1....1..2....0..2....1..0....0..1....1..2....2..0....2..0....0..2....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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