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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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3
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0, 0, 0, 0, 8, 9862, 1067638, 55488142, 3374967940, 239187240144, 15360134570696, 964730606632516, 61989683445413228, 4005716717182224826, 255967892553030600920, 16378998506224697063588, 1050504687249683771795632, 67351449674771471216148786, 4314151246752166099728445868, 276453522147273309254029785276, 17717606001764726850971209939188, 1135386328785418512845166305951994, 72754625853111517738642395445641832, 4662311340698795306229004946849255108, 298772700964630993744576968415214630040, 19145888052227167790585189427230454709502, 1226902568798073025855948189578313739199398, 78622502118507651703659030426757524782646558, 5038287048556094010756276060713112469110084532, 322863244258188584511076820531771298243292346804, 20689713115693125810120458424283134088711708746418, 1325838052128808846982470604742513077251389064878480, 84962322582242436449028078490147227914653412498469176, 5444553480688572729507994773339404670293124094670063400, 348897761885575809340513599895637906535045836867112425442, 22358059291249098112956347313304579317330515128430578229580, 1432748662105938633370488721737295472216003424322051173765262, 91813368745075979865082473968848043302481279531417429418851766, 5883582334056740305836749071273843581025553554521365508472081512, 377031597006006571424070743308269493020186682009428464253448495336
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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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Table of n, a(n) for n=1..40.
J. de Ruiter, Counting Domino Coverings and Chessboard Cycles, 2010.
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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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A070030 deals with 3 X 2n boards, A175855 with 5 X 2n boards.
Sequence in context: A217025 A055308 A188890 * A165429 A079235 A134373
Adjacent sequences: A175878 A175879 A175880 * A175882 A175883 A175884
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KEYWORD
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nonn
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AUTHOR
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Johan de Ruiter, Dec 05 2010
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STATUS
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approved
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