Tribonacci partition formulas modulo m

Each Tribonacci sequence starting with an arbitrary triple of integers is periodic modulo m for any modulus m > 1. For a given m, the mapping between the set S of all m 3 triples of initial values and the set of their coresponding periods define a partition of the set S. In this paper we shall investigate some basic questions related to these partitions from the point of view of enumerative combinatorics