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.
POINTED PRINCIPALLY ORDERED REGULAR SEMIGROUPS
An ordered semigroup S is said to be principally ordered if, for every x ∈ S there exists x⋆ = max {y ∈ S | xyx 6 x}. Here we investigate those principally ordered regular semigroups that are pointed in the sense that th...
An ideal-based zero-divisor graph of direct products of commutative rings
In this paper, specifically, we look at the preservation of the diameter and girth of the zero-divisor graph with respect to an ideal of a commutative ring when extending to a finite direct product of commutative rings....
Relative determinant of a bilinear module
The aim of the paper is to generalize the (ultra-classical) notion of the determinant of a bilinear form to the class of bilinear forms on projective modules without assuming that the determinant bundle of the module is...
ZERO-DIVISOR GRAPHS OF REDUCED RICKART ∗-RINGS
For a ring A with an involution ∗, the zero-divisor graph of A, Γ∗ (A), is the graph whose vertices are the nonzero left zero-divisors in A such that distinct vertices x and y are adjacent if and only if xy∗ = 0. In this...
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.