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.
Authors and Affiliations
Keywords
Related Articles
- EP ID EP576517
- DOI -
- Views 48
- Downloads 0
DEVELOPED ZARISKI TOPOLOGY-GRAPH
In this paper, we introduce the developed Zariski topology-graph associated to an R-module M with respect to a subset X of the set of all quasi-prime submodules of M and investigate the relationship between the algebraic...
BI-INTERIOR IDEALS OF Γ-SEMIRINGS
In this paper, as a further generalization of ideals, we introduce the notion of bi-interior ideal as a generalization of quasi ideal, bi-ideal and interior ideal of Γ-semiring and study the properties of bi-interior ide...
Spectra of R-Vertex Join and R-Edge Join of Two Graphs
The R-graph R(G) of a graph G is the graph obtained from G by introducing a new vertex ue for each e ∈ E(G) and making ue adjacent to both the end vertices of e. In this paper, we determine the adjacency, Laplacian and s...
M-SOLID GENERALIZED NON-DETERMINISTIC VARIETIES
A generalized non-deterministic hypersubstitution is a mapping which maps operation symbols of type τ to the set of terms of the same type which does not necessarily preserve the arity. We apply the generalized nondeterm...
ON L-FUZZY MULTIPLICATION MODULES
Let L be a complete lattice. In a manner analogous to a commutative ring, we introduce and investigate the L-fuzzy multiplication modules over a commutative ring with non-zero identity. The basic properties of the prime...