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 29
- Downloads 0
TRACE INEQUALITIES FOR POSITIVE SEMIDEFINITE MATRICES
Certain trace inequalities for positive definite matrices are generalized for positive semidefinite matrices using the notion of the group generalized inverse.
ON THE UNRECOGNIZABILITY BY PRIME GRAPH FOR THE ALMOST SIMPLE GROUP PGL(2, 9)
The prime graph of a finite group G is denoted by Γ(G). Also G is called recognizable by prime graph if and only if each finite group H with Γ(H) = Γ(G), is isomorphic to G. In this paper, we classify all finite groups w...
Sublattices corresponding to very true operators in commutative basic algebras
We introduce the concept of very true operator on a commutative basic algebra in a way analogous to that for fuzzy logics. We are motivated by the fact that commutative basic algebras form an algebraic axiomatization of...
SEMIGROUPS DERIVED FROM (Γ, N)-SEMIHYPERGROUPS AND T-FUNCTOR
The main purpose of this paper is to introduce the concept of (Γ, n)- semihypergroups as a generalization of hypergroups, as a generalization of nary hypergroups and obtain an exact covariant functor between the category...
ON A PERIODIC PART OF PSEUDO-BCI-ALGEBRAS
In the paper the connections between the set of some maximal elements of a pseudo-BCI-algebra and deductive systems are established. Using these facts, a periodic part of a pseudo-BCI-algebra is studied.