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Problem with rearanging list with paired letters next to each others

Can anybody help?Here's the code that gives me a hedeache for second day 
If I have letter_list = ["a","a",,"b","b","c","c"] it's working
correctly but if I have three or more of any letters for
example:letter_list = ["a","a","a","b","b","c","c"], I'm ending up with
some pairs somewhere.
I took another way approach today:, was thinking
about iterating and checking if neighbour characters won't make a pair
but I've end up with error:
if x != letter_list[i+1] and letter_list[i-1]:
IndexError: list index out of range
andin addition: got 4 "a" (had 3only) and missing 1 "b" :-/