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A208044
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Number of n X 3 0..3 arrays with new values 0..3 introduced in row major order and no element equal to any horizontal, vertical or antidiagonal neighbor (colorings ignoring permutations of colors).
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2
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2, 8, 44, 244, 1356, 7540, 41932, 233204, 1296972, 7213172, 40116428, 223109620, 1240835916, 6900974452, 38380133836, 213453141236, 1187130917964, 6602291295860, 36718991727308, 204214611724276, 1135750348251468
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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) = 7*a(n-1) - 8*a(n-2) for n>3.
G.f.: 2*x*(1 - x)*(1 - 2*x) / (1 - 7*x + 8*x^2).
a(n) = (2^(-5-n)*((7-sqrt(17))^n*(-13+5*sqrt(17)) + (7+sqrt(17))^n*(13+5*sqrt(17)))) / sqrt(17) for n>1.
(End)
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EXAMPLE
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Some solutions for n=4:
0 1 0 0 1 0 0 1 2 0 1 0 0 1 2 0 1 0 0 1 2
2 3 2 2 3 1 2 0 3 2 3 1 2 3 0 2 3 1 2 3 0
1 0 1 1 2 0 3 1 2 0 2 0 0 1 3 0 2 3 0 1 2
2 3 2 3 1 2 0 3 1 1 3 1 2 0 1 3 1 2 2 3 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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