Do you mean to say there are 9 choose 4 == 126 possible combinations for a 3x3 pattern? I think this would only be true if you could use a maximum of four dots in the pattern, which isn't the case.

Although calculating it this way will double-count some patterns which include long lines, I would say that there ar far closer to 9! == 362880 passwords. Even if long lines cut that space in half, 150000 more than meets your minimum of 15^4.