If a sequence repeats itself, and you want to see the number of unique permutations there are then the formula is:
Rotation Symmetry
Mirror Symmetry
Intuition
Suppose you have a table with 4 seats and 4 people to be seated.
The possible seating arrangements before dedup is
To remove all the duplicates, think about the # of times it could be shuffled around and still have the same order (person to the left is still to the left after a shuffle)
So, divide by 4 and you get