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A233162
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Number of n X 1 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, diagonally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 4 5 and 6, 2 appearing before 3 4 and 5, and 3 appearing before 4 in row major order (unlabelled 8-colorings with no clashing color pairs).
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7
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1, 1, 3, 11, 48, 236, 1248, 6896, 39168, 226496, 1325568, 7821056, 46399488, 276294656, 1649369088, 9862639616, 59041579008, 353712521216, 2120127479808, 12712174616576, 76238687305728, 457294683570176, 2743218342985728
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OFFSET
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1,3
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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) -44*a(n-2) +48*a(n-3) for n>4.
G.f.: x*(1 - 11*x + 35*x^2 - 29*x^3) / ((1 - 2*x)*(1 - 4*x)*(1 - 6*x)).
a(n) = (2^(n-6)*(90 + 9*2^n + 2*3^n)) / 9 for n>1.
(End)
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EXAMPLE
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Some solutions for n=5:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....1....1....1....1....1....1....1....1....1....1....1....1....1
..7....7....2....0....2....2....2....2....2....7....2....2....7....0....2....0
..6....2....6....2....6....7....1....7....7....1....6....0....2....1....6....2
..7....0....3....6....7....3....2....5....1....2....2....6....6....7....0....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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