Abstract
The sedenions form a 16-dimensional Cayley-Dickson algebra. In this paper, we introduce the Tribonacci and Tribonacci-Lucas sedenions. Furthermore, we present some properties of these sedenions and derive relationships between them.
Highlights
The Tribonacci sequence { Tn }n≥0 and the Tribonacci-Lucas sequence {Kn }n≥0 are defined by the third-order recurrence relations: Tn = Tn−1 + Tn−2 + Tn−3, T0 = 0, T1 = 1, T2 = 1, (1)
We present some information on Cayley-Dickson algebras
Efficient algorithms for the multiplication of quaternions, octonions, and sedenions with a reduced number of real multiplications already exist, and the results of synthesizing an efficient algorithm of computing the two 2n -ions product are given in the following Table 2
Summary
The Tribonacci sequence { Tn }n≥0 and the Tribonacci-Lucas sequence {Kn }n≥0 are defined by the third-order recurrence relations: Tn = Tn−1 + Tn−2 + Tn−3 , T0 = 0, T1 = 1, T2 = 1,. We present the first few values of the Tribonacci and Tribonacci-Lucas numbers with positive and negative subscripts: n. It is well known that for all integers n, the usual Tribonacci and Tribonacci-Lucas numbers can be expressed using Binet’s formulas: Tn =. We present some properties of the Tribonacci and Tribonacci-Lucas numbers. We define Tribonacci and Tribonacci-Lucas sedenions and give some properties of them. Before giving their definition, we present some information on Cayley-Dickson algebras.
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