Expected Patterns in Permutation Classes

In the set of all patterns in $S_n$, it is clear that each k-pattern occurs equally often. If we instead restrict to the class of permutations avoiding a specific pattern, the situation quickly becomes more interesting. Mikl'os B'ona recently proved that, surprisingly, if we consider the class of permutations avoiding the pattern 132, all other non-monotone patterns of length 3 are equally common. In this paper we examine the class $\text{Av}(123)$, and give exact formula for the occurrences of each length 3 pattern. While this class does not break down as nicely as $\text{Av}(132)$, we find some interesting similarities between the two and prove that the number of 231 patterns is the same in each.