28 Mar
2014
28 Mar
'14
10:16 a.m.
="Warren D Smith" <warren.wds@gmail.com> What is the distance between (x1,y1) and (x2,y2) measured in number of knight-moves?
Warren, some years ago I put some "knight metric" sequences in the OEIS. Special-cases to compare with your conjecture: dx,dy =... ...n,0: http://oeis.org/A018837 2[ (n+2)/4 ] if n even, 2[ (n+1)/4 ]+1 if n odd (n >= 8) ...n,n: http://oeis.org/A018839 2*ceiling(n/3), n >= 3 Also perhaps of interest is the size of the n-move neighborhood, etc. The OEIS has some references as well. Search on "knight" gives many hits. "Enjoy"! --MLB