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.