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A187859
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Number of 4-step one space for components leftwards or up, two space for components rightwards or down asymmetric quasi-queen's tours (antidiagonal moves become knight moves) on an n X n board summed over all starting positions.
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1
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0, 0, 216, 968, 2754, 5428, 9237, 14040, 19837, 26628, 34413, 43192, 52965, 63732, 75493, 88248, 101997, 116740, 132477, 149208, 166933, 185652, 205365, 226072, 247773, 270468, 294157, 318840, 344517, 371188, 398853, 427512, 457165, 487812
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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) = 497*n^2 - 2652*n + 3448 for n>5.
G.f.: x^3*(216 + 320*x + 498*x^2 - 146*x^3 + 247*x^4 - 141*x^5) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.
(End)
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EXAMPLE
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Some solutions for 4 X 4:
..0..0..0..0....3..2..4..0....0..0..0..0....0..4..0..0....0..0..0..4
..0..0..0..0....0..1..0..0....0..4..3..0....0..0..3..0....0..3..2..0
..4..3..2..0....0..0..0..0....2..1..0..0....1..0..2..0....0..0..0..1
..0..0..1..0....0..0..0..0....0..0..0..0....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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