  A general n-state directed `sandpile' model is introduced. The stationary
properties of the n-state model are derived for n < infty, and analytical
arguments based on a central limit theorem show that the model belongs to the
universality class of the totally asymmetric Oslo model, with a crossover to
uncorrelated branching process behavior for small system sizes. Hence, the
central limit theorem allows us to identify the existence of a large
universality class of one-dimensional directed sandpile models.
