A function ψ:R→R is said to be a Tribonacci function with period p if ψ(x+3p)=ψ(x+2p)+ψ(x+p)+ψ(x), for all x∈R. In this paper, we present some properties on the Tribonacci functions with period p. We show that if ψ is a Tribonacci function with period p, then limx→∞ψ(x+p)/ψ(x)=β, where β is the root of the equation x3-x2-x-1=0 such that 1<β<2.

In this article, we establish a link between the values of a frieze of type D n and some values of a particular frieze of type A 2n−1 . This link allows us to compute, independently of each other, all the cluster variables in the cluster algebra associated with a quiver Q of type D n .