QUADRATIC APPROXIMATION OF GENERALIZED TRIBONACCI SEQUENCES
Journal Title: Discussiones Mathematicae - General Algebra and Applications - Year 2018, Vol 38, Issue 2
Abstract
In this paper, we give quadratic approximation of generalized Tribonacci sequence {Vn}n≥0 defined by Vn = rVn−1 + sVn−2 + tVn−3 (n ≥ 3) 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. Keywords: Binet’s formula, companion matrix, generalized Tribonacci sequence, Narayana number, Padovan number, quadratic approximation, Tribonacci number. 2010 Mathematics Subject Classification: Primary: 11B39; Secondary: 15A24, 40C05.
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