THE GENERALIZED TRIBONACCI p-NUMBERS AND APPLICATIONS

Abstract

The generalized tribonacci p-numbers (p ∈ N), which generalizes the

tribonacci numbers, are integers satisfying

Tp(n + 2) = Tp(n + 1) + Tp(n) + Tp(n − p).

We construct the companion matrix for the generalized tribonacci p

numbers and derive some interesting identities. Several explicit formulas

for the tribonacci p-numbers are also derived using the tribonacci p

triangle.