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Knight's tour is very well known problem, but what about rook's tour? On $n\times1$ chessboard there are obviously $n!$ open and $(n-1)!$ closed tours.

Is there a way to easily compute number of open and closed rook's tours on $n\times m$ (or just for some small $m$) chessboard? Question doesn't look trivial, so I don't know what can be added to make it more informative. I will appreciate any references.

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    $\begingroup$ See A096121 for $n\times2$ and A096970 for $n\times n$. $\endgroup$ – bof Feb 4 at 0:51
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    $\begingroup$ Forgot to mention, those references are for open tours. I didn't see anything on closed tours. $\endgroup$ – bof Feb 4 at 0:59
  • $\begingroup$ @bof, thank you very much! $\endgroup$ – user514787 Feb 4 at 12:59
  • $\begingroup$ @bof, can you please also (if you have time) look for a proof of $n\times2$? $\endgroup$ – user514787 Feb 8 at 16:37

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