# Number of open and closed rook's tours

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.

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