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A184368
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1/3 the number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock having at least two equal elements connected horizontally or vertically.
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2
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21, 153, 1107, 8019, 58077, 420633, 3046491, 22064643, 159806277, 1157419449, 8382773187, 60713414163, 439725443661, 3184773389433, 23066169329547, 167059976482179, 1209955382858997, 8763272085493593, 63469230958692531
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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) + 9*a(n-2).
G.f.: 3*x*(7 + 9*x) / (1 - 6*x - 9*x^2).
a(n) = ((3-3*sqrt(2))^n*(-4+3*sqrt(2)) + (3*(1+sqrt(2)))^n*(4+3*sqrt(2))) / (2*sqrt(2)).
(End)
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EXAMPLE
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Some solutions for 3 X 2 with a(1,1)=0:
..0..0....0..0....0..1....0..0....0..0....0..1....0..1....0..2....0..1....0..0
..1..0....2..2....1..1....2..1....0..2....0..0....2..1....0..2....0..1....1..2
..2..0....1..1....2..0....0..0....0..2....0..2....2..2....0..2....0..2....1..0
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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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