We consider the problem of enumerating periodic $\sigma$-juggling sequences of length $n$ for multiplex juggling, where $\sigma$ is the initial state (or $landing ~ schedule$) of the balls. We first show that this problem is equivalent to choosing 1's in a specified matrix to guarantee certain column and row sums, and then using this matrix, derive a recursion. This work is a generalization of earlier work of Fan Chung and Ron Graham. \\ This is joint work with Ron Graham.