Quadratic Approximation of Generalized Tribonacci Sequences

Abstract

In this paper, we give quadratic approximation of generalized Tribonacci sequence {Vn}n≥0 defined by Vn = rVn−1 + sV n−2 + tV n−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
• primary: 11b39
• secondary: 15a24, 40c05