  We consider the problem of enumerating periodic $\sigma$-juggling sequences
of length $n$ for multiplex juggling, where $\sigma$ is the initial state (or
{\em 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.
