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A175881 Number of closed Knight's tours on a 6 X n board. 4
0, 0, 0, 0, 8, 9862, 1067638, 55488142, 3374967940, 239187240144, 15360134570696, 964730606632516, 61989683445413228, 4005716717182224826, 255967892553030600920, 16378998506224697063588, 1050504687249683771795632, 67351449674771471216148786, 4314151246752166099728445868 (list; graph; refs; listen; history; text; internal format)



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


Johan de Ruiter, Table of n, a(n) for n = 1..40

J. de Ruiter, Counting Domino Coverings and Chessboard Cycles, 2010.


The smallest 6 X n board admitting a closed Knight's tour is the 6 X 5, on which there are 8 such tours.


A070030 deals with 3 X 2n boards, A175855 with 5 X 2n boards.

Sequence in context: A230570 A055308 A188890 * A165429 A242852 A079235

Adjacent sequences:  A175878 A175879 A175880 * A175882 A175883 A175884




Johan de Ruiter, Dec 05 2010



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Last modified November 26 10:39 EST 2015. Contains 264502 sequences.