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A187513
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Number of 8-step S, E, and NW-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, 12, 390, 1910, 4880, 9250, 14969, 22026, 30421, 40154, 51225, 63634, 77381, 92466, 108889, 126650, 145749, 166186, 187961, 211074, 235525, 261314, 288441, 316906, 346709, 377850, 410329, 444146, 479301, 515794, 553625, 592794, 633301
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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) = 669*n^2 - 4316*n + 6681 for n>6.
Empirical g.f.: x^3*(12 + 354*x + 776*x^2 + 308*x^3 - 50*x^4 - 51*x^5 - 11*x^6) / (1 - x)^3. - Colin Barker, Nov 27 2017
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EXAMPLE
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Some solutions for 4X4
..0..7..8..0....0..0..0..0....0..0..0..0....1..0..0..0....5..0..0..0
..4..5..6..0....3..4..5..6....5..0..0..0....2..6..7..8....6..4..2..0
..0..3..1..0....0..2..0..7....6..4..2..0....3..4..5..0....7..8..3..1
..0..0..2..0....0..0..1..8....7..8..3..1....0..0..0..0....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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