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A175881
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Number of closed Knight's tours on a 6 X n board.
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4
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0, 0, 0, 0, 8, 9862, 1067638, 55488142, 3374967940, 239187240144, 15360134570696, 964730606632516, 61989683445413228, 4005716717182224826, 255967892553030600920, 16378998506224697063588, 1050504687249683771795632, 67351449674771471216148786, 4314151246752166099728445868
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OFFSET
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1,5
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COMMENTS
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Could you please say how you calculated these numbers? - N. J. A. Sloane, Dec 05 2010?
I kept track of pairs of loose ends within the two rightmost columns of a 6 X n board, assuming that everything to the left of these two columns is fully connected and that there are no cycles (or one if this is a final state). Next I added a new column and connected it to the rightmost two columns in all ways such that there are no cycles formed(or one if this results in a final state) and the leftmost column in the current state is fully connected and can be dropped. From this followed a transition matrix. I can provide a reference to my writeup once it is completed and has been accepted by my supervisor. - Johan de Ruiter, Dec 05 2010
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LINKS
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EXAMPLE
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The smallest 6 X n board admitting a closed Knight's tour is the 6 X 5, on which there are 8 such tours.
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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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