Yes, these are "combinations" since you are treating all "2"s as the same.

And, of course, the distinction between "0" and "1" is irrelevant. The number of ways you can have a string of 1 "2" and 13 "other" is . The number of ways you can have 3 "2"s and 11 "other" is , etc. The number of ways you can write and odd number of "2"s and fill out the remaining places with "other" is .