Determine the Pattern

Hello: I need help finding the pattern for the attached file. If you can do it, and the pattern holds. I will award you the $50 I am offering to find it. Again, the $50 is only awarded if the pattern can be found, and it matches all cases in the attached image. Description about the attached PDF: - The "Output" column -- the third column -- is the only pattern I'm trying to find. - The "# of A's" and the "# of B's" columns MAY help in determining the pattern; I'm not sure. - The "Example Output" column is a combination of the "Output Column" and the "# of A's" and the "# of B's." I provide it, so the TRUE output can be seen and helps with determining the pattern.