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A187589
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Number of 6-step E, S, NW and NE-moving king's tours on an n X n board summed over all starting positions.
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1
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0, 0, 104, 1069, 3514, 7480, 12874, 19696, 27946, 37624, 48730, 61264, 75226, 90616, 107434, 125680, 145354, 166456, 188986, 212944, 238330, 265144, 293386, 323056, 354154, 386680, 420634, 456016, 492826, 531064, 570730, 611824, 654346, 698296
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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) = 714*n^2 - 3888*n + 5104 for n>4.
G.f.: x^3*(104 + 757*x + 619*x^2 + 41*x^3 - 93*x^4) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>7.
(End)
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EXAMPLE
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Some solutions for 4 X 4:
..0..0..0..0....0..0..0..6....0..0..0..4....0..1..2..0....0..0..6..0
..0..0..6..0....0..4..5..0....0..2..3..5....0..0..3..0....1..3..4..5
..1..3..4..5....0..1..3..0....0..0..1..6....0..0..4..5....2..0..0..0
..2..0..0..0....0..2..0..0....0..0..0..0....0..0..0..6....0..0..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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