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A187302
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Number of 7-step one space leftwards or up, two space rightwards or down asymmetric rook's tours on an n X n board summed over all starting positions.
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1
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0, 0, 108, 1368, 6264, 15596, 31172, 52256, 79634, 112568, 151266, 195512, 245332, 300704, 361628, 428104, 500132, 577712, 660844, 749528, 843764, 943552, 1048892, 1159784, 1276228, 1398224, 1525772, 1658872, 1797524, 1941728, 2091484, 2246792
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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) = 2776*n^2 - 19580*n + 30728 for n>11.
G.f.: 2*x^3*(54 + 522*x + 1242*x^2 + 400*x^3 + 904*x^4 - 368*x^5 + 393*x^6 - 369*x^7 + 104*x^8 - 108*x^9 + 13*x^10 - 11*x^11) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>14.
(End)
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EXAMPLE
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Some solutions for 4 X 4:
..0..0..0..0....0..0..2..1....0..0..0..0....0..2..1..3....0..0..0..0
..5..4..6..0....0..5..7..6....0..4..3..5....0..7..0..0....7..0..0..1
..0..3..2..1....0..4..3..0....1..0..2..0....0..6..5..4....6..5..0..0
..0..0..7..0....0..0..0..0....0..0..7..6....0..0..0..0....0..4..3..2
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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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