Meanwhile, E.Clark's tip led me to find the "Encyclopedia of Distances" by Michel Marie Deza, Elena Deza, published by Springer 2009. Amazingly enough, on page 336 it says:
The Knight distance... is 3 if (M,m)=(1,0); is 4 if (M,m)=(2,2); otherwise equals max( ceiling(M/2), ceiling((M+m)/3)) + (M+m) - max(ceiling(M/2), ceiling(((M+m)/3)) mod 2 where M>=m>=0.
--Unfortunately the Encyclopedia's formula is wrong since it thinks KnightDist(3,0) = 5, whereas actually it is 3. But this was merely a typo, which we can correct by inserting parentheses []: CORRECTED: The Knight distance... is 3 if (M,m)=(1,0); is 4 if (M,m)=(2,2); otherwise equals max( ceiling(M/2), ceiling((M+m)/3)) + [(M+m) - max(ceiling(M/2), ceiling(((M+m)/3))] mod 2 where M>=m>=0.