[omk3]

Ok, here's my try:

Spoiler:

Each time we add 10 to each digit. If we get same numbers side by side, we keep only one of them, updating the tens digit to the number of same numbers (I'm not at all happy with how I phrased it, but it works)

So
1
11
11 11 (adding 10 to each digit of the above number. We get 2 11s, so we make them 21)
12 11
11 12 11 11, which again makes 11 12 21
11 11 11 12 12 11, which makes 31 (3 11s) 22 (2 12s) 11
13 11 12 12 11 11, which makes 13 11 22 21
which brings us to the next number, which should be:
11 13 11 11 12 12 12 11, thus 11 13 21 32 11.