DNA chromosome combinations

this "problem" is not based on fact.

In one DNA string there is room for 13 cromosoms.

One string have 13 places, the first, second,3,4,5,6...13.

There is three groups of cromosoms, A,B,C.

The A cromosomes can be placed 1,2,3 or 4 in a row. (there can be more than four on one string but maximum 4 in a row, AND just one row with 4 on one string! But 3rows with three is possible, you know what I mean)(AAABAAABAAACC)

The B cromosomes can be placed 1,2 or 3 in a row. On one string there can be maximum 2 rows with 3 B cromosomes, but of course not after each other BBBBBB.)

The C cromosomes can be placed 1,2 or 3 in a row. On one string there can be maximum 1 row with 3 C.

So, the question is: How many possibilities are there to put a DNA string together?

Accepted examples: AAAABAAACCCBB, BBBAAAABBBCAB...

the only combination that is not valid is the ones with 4A,2x3B and 3C.

example: AAAABBBCCCBBB, BBBAAAACCCBBB...

Need help with this, I don't know the answer, please show how to solve this(Nod)