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A187174
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Number of 4-step left-handed knight's tours (moves only out two, left one) on an n X n board summed over all starting positions.
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1
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0, 0, 0, 8, 48, 176, 384, 664, 1016, 1440, 1936, 2504, 3144, 3856, 4640, 5496, 6424, 7424, 8496, 9640, 10856, 12144, 13504, 14936, 16440, 18016, 19664, 21384, 23176, 25040, 26976, 28984, 31064, 33216, 35440, 37736, 40104, 42544, 45056, 47640, 50296
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OFFSET
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1,4
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LINKS
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FORMULA
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Empirical: a(n) = 36*n^2 - 260*n + 440 for n>5.
G.f.: 8*x^4*(1 + 3*x + 7*x^2 - x^3 - x^4) / (1 - x)^3 (conjectured). - Colin Barker, Apr 22 2018
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EXAMPLE
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Some solutions for 4 X 4:
..0..0..1..0....0..0..3..0....0..0..4..0....0..0..2..0....0..0..1..0
..4..0..0..0....4..0..0..0....3..0..0..0....1..0..0..0....2..0..0..0
..0..0..0..2....0..0..0..2....0..0..0..1....0..0..0..3....0..0..0..4
..0..3..0..0....0..1..0..0....0..2..0..0....0..4..0..0....0..3..0..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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