Quadratic Approximation of Generalized Tribonacci Sequences
Abstract
In this paper, we give quadratic approximation of generalized Tribonacci sequence \Vn\n≥0 defined by Eq. (eq:7) and use this result to give the matrix form of the n-th power of a companion matrix of \Vn\n≥0. Then we re-prove the cubic identity or Cassini-type formula for \Vn\n≥0 and the Binet's formula of the generalized Tribonacci quaternions.
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