This is what I think:
You have 8 colors and 8 squares across, so you can pick any sequence, then for the next row move the first color to the end, the 2nd to the 1st, etc. The third will have the previous 2nd color (now the 1st color) moved to the end. I can picture this, but it is very hard to explain. Does it make sense?
Jints, you posted your reply while I was writing -- your response really makes sense, and is so easy to understand.