Quadratic Approximation of Generalized Tribonacci Sequences

Abstract

In this paper, we give quadratic approximation of generalized Tribonacci sequence $\{V_n{\}}_{n\ge 0}$ defined by Eq. (\ref{eq:7}) and use this result to give the matrix form of the $n$-th power of a companion matrix of $\{V_n{\}}_{n\ge 0}$. Then we re-prove the cubic identity or Cassini-type formula for $\{V_n{\}}_{n\ge 0}$ and the Binet's formula of the generalized Tribonacci quaternions.

arXiv comment10 pages

Cited by in corpus (1)

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