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%I #21 Nov 25 2014 04:43:36
%S 0,0,0,0,8,9862,1067638,55488142,3374967940,239187240144,
%T 15360134570696,964730606632516,61989683445413228,4005716717182224826,
%U 255967892553030600920,16378998506224697063588,1050504687249683771795632,67351449674771471216148786,4314151246752166099728445868
%N Number of closed Knight's tours on a 6 X n board.
%C Could you please say how you calculated these numbers? - _N. J. A. Sloane_, Dec 05 2010?
%C 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
%H Johan de Ruiter, <a href="/A175881/b175881.txt">Table of n, a(n) for n = 1..40</a>
%H J. de Ruiter, <a href="http://www.math.leidenuniv.nl/~jruiter/CountingDominoCoveringsAndChessboardCycles.pdf">Counting Domino Coverings and Chessboard Cycles</a>, 2010.
%e The smallest 6 X n board admitting a closed Knight's tour is the 6 X 5, on which there are 8 such tours.
%Y A070030 deals with 3 X 2n boards, A175855 with 5 X 2n boards.
%K nonn
%O 1,5
%A _Johan de Ruiter_, Dec 05 2010
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