All Research Papers Published In The Fibonacci Quarterly

Research Article
1
10.1080/00150517.2020.12427556

On the Relation Between Fibonacci and Lucas Numbers

Dec 01, 2020
The Fibonacci Quarterly
Spiros D Dafnis

Research Article
4
10.1080/00150517.2020.12427561

Deterministic Zeckendorf Games

Dec 01, 2020
The Fibonacci Quarterly
Ruoci Li + 6 more +6

Research Article
5
10.1080/00150517.2020.12427551

Matrices in the Determinant Hosoya Triangle

Dec 01, 2020
The Fibonacci Quarterly
Matthew Blair + 3 more +3

Research Article
1
10.1080/00150517.2020.12427566

New Identities for Some Symmetric Polynomials, and a Higher Order Analogue of the Fibonacci and Lucas Numbers

Dec 01, 2020
The Fibonacci Quarterly
Genki Shibukawa

Research Article
1
10.1080/00150517.2020.12427559

Recursive Triangles Appearing Embedded in Recursive Families

Dec 01, 2020
The Fibonacci Quarterly
Russell Jay Hendel

Research Article
10.1080/00150517.2020.12427570

A Report on the 19th International Conference on Fibonacci Numbers and Their Applications

Nov 01, 2020
The Fibonacci Quarterly
Marjorie Bicknell Johnson

Research Article
1
10.1080/00150517.2020.12427576

Generalized Fibonacci Sequences in Pythagorean Triple Preserving Matrices

Nov 01, 2020
The Fibonacci Quarterly
Jathan Austin + 1 more +1

Research Article
1
10.1080/00150517.2020.12427584

Central Limit Theorems for Compound Paths on the Two-Dimensional Lattice

Aug 01, 2020
The Fibonacci Quarterly
Evan Fang + 7 more +7

Research Article
10.1080/00150517.2020.12427594

Cycles of Sums of Integers

May 01, 2020
The Fibonacci Quarterly
Bruno Dular

We study the period of the linear map $T:\mathbb{Z}_m^n\rightarrow \mathbb{Z}_m^n:(a_0,\dots,a_{n-1})\mapsto(a_0+a_1,\dots,a_{n-1}+a_0)$ as a function of $m$ and $n$, where $\mathbb{Z}_m$ stands for the ring of integers modulo $m$. Since this map is a variant of the Ducci sequence, several known results are adapted in the context of $T$. The main theorem of this paper states that the period modulo $m$ can be deduced from the prime factorization of $m$ and the periods of its prime factors. We also characterize the tuples that belong to a cycle when $m$ is prime.

Research Article
10.1080/00150517.2020.12427595

A Nonlinear Recurrence and Its Relations to Chebyshev Polynomials

May 01, 2020
The Fibonacci Quarterly
Roger C Alperin