Knight moves

[arcnets]

Hi all,
I found this problem in a Martin Gardner book. You have a chess board of n x n squares. How many moves m(n) can a chess knight make on this board without crossing or touching its own path?

m(0) = 0
m(1) = 0
m(2) = 0
m(3) = 2
m(4) = 5
m(5) = 10
m(6) = 17
m(7) = 24
m(8) = 35

http://home.t-online.de/home/b_c.kuss/mgard.JPG

Anyone know how to continue this? Thanks!

[On Radioactive Waves]

Make a 9x9 board, and try it. You should be able to make more than 35 moves.

[plus]

How does it change also for a m x n board?