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A187288
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Number of 3-step one or two space at a time rook's tours on an n X n board summed over all starting positions.
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1
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0, 8, 108, 328, 672, 1128, 1696, 2376, 3168, 4072, 5088, 6216, 7456, 8808, 10272, 11848, 13536, 15336, 17248, 19272, 21408, 23656, 26016, 28488, 31072, 33768, 36576, 39496, 42528, 45672, 48928, 52296, 55776, 59368, 63072, 66888, 70816, 74856, 79008
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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Empirical: a(n) = 56*n^2 - 160*n + 72 for n>3.
G.f.: 4*x^2*(2 + 21*x + 7*x^2 + x^3 - 3*x^4) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>6.
(End)
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EXAMPLE
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Some solutions for 4 X 4:
..0..0..0..0....0..0..0..0....0..0..0..0....3..0..0..0....0..0..3..2
..2..0..0..0....0..0..0..0....0..0..0..0....2..0..1..0....0..0..0..1
..1..0..0..0....0..0..1..0....1..0..0..0....0..0..0..0....0..0..0..0
..3..0..0..0....3..0..2..0....2..0..3..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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