Quadratic approximation of generalized Tribonacci sequences
Copyright policy )Quadratic approximation of generalized Tribonacci sequences
In this paper, we give quadratic approximation of generalized Tribonacci sequence $\{V_{n}\}_{n\geq0}$ 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 $\{V_{n}\}_{n\geq0}$. Then we re-prove the cubic identity or Cassini-type formula for $\{V_{n}\}_{n\geq0}$ and the Binet's formula of the generalized Tribonacci quaternions.
10 pages
companion matrix, tribonacci number, secondary: 15a24, 40c05, binet’s formula, generalized tribonacci sequence, narayana number, primary: 11b39, 11B39, 15A24, 40C05, quadratic approximation, QA1-939, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), padovan number, Mathematics
companion matrix, tribonacci number, secondary: 15a24, 40c05, binet’s formula, generalized tribonacci sequence, narayana number, primary: 11b39, 11B39, 15A24, 40C05, quadratic approximation, QA1-939, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), padovan number, Mathematics
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