Results 41 to 50 of about 1,240,285 (142)
A Closed Formula for the Sums of Squares of Generalized Tribonacci numbers [PDF]
, 2020 In this paper, closed forms of the sum formulas for the squares of generalized Tribonacci numbers are presented. As special cases, we give summation formulas of the squares of Tribonacci, Tribonacci-Lucas, Padovan, Perrin, Narayana and some other third ...
Soykan, Yüksel
core +2 more sources
On the Characteristic Polynomial of the Generalized k-Distance Tribonacci Sequences
Mathematics, 2020 In 2008, I. Włoch introduced a new generalization of Pell numbers. She used special initial conditions so that this sequence describes the total number of special families of subsets of the set of n integers.
Pavel Trojovský
doaj +1 more source
Avoiding patterns in irreducible permutations [PDF]
Discrete Mathematics & Theoretical Computer Science, 2016 We explore the classical pattern avoidance question in the case of irreducible permutations, i.e., those in which there is no index $i$ such that $\sigma (i+1) - \sigma (i)=1$.
Jean-Luc Baril
doaj +1 more source
Solutions of the Markoff equation in Tribonacci numbers [PDF]
, 2023 In this paper, we determine all of the positive integer solutions of the so-called Markoff equation x2 + y2 + z2 = 3xyz in the sequence of Tribonacci numbers {Tn}, i.e.
Hashim, Hayder R., Hayder R. Hashim
core +1 more source
On Third‐Order Linear Recurrent Functions
Discrete Dynamics in Nature and Society, Volume 2019, Issue 1, 2019., 2019 A function ψ:R→R is said to be a Tribonacci function with period p if ψ(x + 3p) = ψ(x + 2p) + ψ(x + p) + ψ(x), for all x∈R. In this paper, we present some properties on the Tribonacci functions with period p. We show that if ψ is a Tribonacci function with period p, then limx→∞(ψ(x + p)/ψ(x)) = β, where β is the root of the equation x3 − x2 − x − 1 = 0
Kodjo Essonana Magnani +1 more
wiley +1 more source
Explicit Form of the Inverse Matrices of Tribonacci Circulant Type Matrices
Abstract and Applied Analysis, Volume 2015, Issue 1, 2015., 2015 It is a hot topic that circulant type matrices are applied to networks engineering. The determinants and inverses of Tribonacci circulant type matrices are discussed in the paper. Firstly, Tribonacci circulant type matrices are defined. In addition, we show the invertibility of Tribonacci circulant matrix and present the determinant and the inverse ...
Li Liu, Zhaolin Jiang, Zidong Wang
wiley +1 more source
Total Graph Interpretation of the Numbers of the Fibonacci Type
Journal of Applied Mathematics, Volume 2015, Issue 1, 2015., 2015 We give a total graph interpretation of the numbers of the Fibonacci type. This graph interpretation relates to an edge colouring by monochromatic paths in graphs. We will show that it works for almost all numbers of the Fibonacci type. Moreover, we give the lower bound and the upper bound for the number of all (A1, 2A1)‐edge colourings in trees.
Urszula Bednarz +3 more
wiley +1 more source
Several Determinantal Expressions of Generalized Tribonacci Polynomials and Sequences
, 2020 In the paper, the authors present several explicit formulas for the $(p,q,r)$-Tribonacci polynomials and generalized Tribonacci sequences in terms of the Hessenberg determinants and, consequently, derive several explicit formulas for the Tribonacci ...
Wei Shih Du, Can Kizilates, Feng Qi
core +1 more source
On the Two‐Term Zeckendorf Representations of the Padovan and Perrin Sequences
Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.In this paper, we completely solve the Diophantine equations Pm = Fn + Fk and Em = Fn + Fk under the condition n ≥ k + 2 ≥ 4, where Pm is the m‐th Padovan number, Em is the m‐th Perrin number, and Fk is the k‐th Fibonacci number. This work determines all terms of the Padovan and Perrin sequences that admit a unique two‐term Zeckendorf representation ...
Awaou Lare Ousseni +4 more
wiley +1 more source
Exact Determinants of Some Special Circulant Matrices Involving Four Kinds of Famous Numbers
Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014 Circulant matrix family is used for modeling many problems arising in solving various differential equations. The RSFPLR circulant matrices and RSLPFL circulant matrices are two special circulant matrices. The techniques used herein are based on the inverse factorization of polynomial. The exact determinants of these matrices involving Perrin, Padovan,
Xiaoyu Jiang, Kicheon Hong, Tongxing Li
wiley +1 more source