Counting Queen's paths on a rectangular chessboard
Haskell, 94 91 64 54 bytes



1!1=1;m!n=sum[m!(n-x)+(m-x)!n+(m-x)!(n-x)|x&lt;-[1..m+n]]


Try it online!

Initially a boring port of the comment on OEIS

-27 from some tricks off dingledooper's answer

-10 from Christian Sievers