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A330611
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Number of near-magic (only long lines are magic) knight's tours on a 4 X 2n board.
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0
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OFFSET
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1,3
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COMMENTS
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A semi-magic knight's tour is a tour that adds to a constant sum in every line in one direction, but not in every line in the perpendicular direction. A near-magic tour is a special type of semi-magic tour in which the non-magic direction has the lines add to the magic constant and two other values. Such tours are of interest on boards where magic tours don't exist.
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LINKS
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EXAMPLE
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Example of 4 x 14 near-magic knight's tour. All long lines add to 399 and the short lines add to the magic constant 114 and 114 +- 4.
1 54 25 32 5 52 23 48 9 38 11 40 17 44
28 31 4 53 24 33 6 37 20 47 18 43 14 41
55 2 29 26 51 22 35 8 49 10 39 12 45 16
30 27 56 3 34 7 50 21 36 19 46 15 42 13
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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STATUS
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approved
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