More Identities on the Tribonacci Numbers

Abstract

In this paper, we use a simple method to derive different recurrence relations on the Tribonacci numbers and their sums. By using the companion matrices and generating matrices, we obtain more identities on the Tribonacci numbers and their sums, which are more general than those given in the literature [E. Kilic, Tribonacci Sequences with Certain Indices and Their Sum, Ats Combinatoria \(86 (2008),13-22]\).