|| This talk is about the generators of cluster algebras of rank two, the so-called cluster variables. Cluster variables are certain Laurent polynomials in two variables which are defined in a recursive way. Each of these variables corresponds to a (preprojectiv or preinjective) representation of the quiver with two vertices, 1 and 2, and r arrows from 2 to 1, also known as the generalized Kronecker quiver. I will present a direct formula for the cluster variables in terms of certain subpaths of a specific lattice path. This formula is the result of a joint work with Kyungyong Lee.