Results 181 to 190 of about 717 (218)

Generalized Fibonacci Sequences

The Mathematics Teacher, 2000
Everyone loves the Fibonacci sequence. It is easy to describe, yet it gives rise to a vast amount of substantial mathematics. Physical applications and connections with various branches of mathematics abound. What could be better, unless someone told us that the Fibonacci sequence is but one member of an infinite family of sequences that we could be ...
openaire   +1 more source

The Fibonacci sequence, generalized Fibonacci sequences, and related topics

1995
Abstract One of the most engaging puzzles in the history of mathematics was formulated by Leonardo of Pisa, nicknamed Fibonacci (1170-1250) in his celebrated book Liber abaci: How many pairs of rabbits will be produced in a year, beginning with a single pair, if in every month each pair bears a new pair which becomes productive from the ...
openaire   +1 more source

Duplications In the \(k\)-generalized Fibonacci sequences

2021
Let \(k \geq 2\) be an integer. The \(k\)-generalized Fibonacci sequence \(({F_n}^{(k)})_{n \in\mathbb{Z}}\) has the initial values \[ F_{-k+2}^{(k)}=\dots=F_{0}^{(k)}=0,\quad F_{1}^{(k)}=1, \] and satisfies the recurrence \[ F_{n}^{(k)}=F_{n-1}^{(k)}+\dots+F_{n-k}^{(k)} \text{ for all } n \in\mathbb{Z}.
Luca, Florian, Pethő, Attila, Szalay, László   +2 more
openaire   +1 more source

On equivalence classes of generalized Fibonacci sequences

J. Integer Seq., 2016
Summary: We consider a generalized Fibonacci sequence \((G_n)\) by \(G_1, G_2 \in \mathbb{Z} \) and \(G_n = G_{n-1} + G_{n-2}\) for any integer \(n\). Let \(p\) be a prime number and let \(d(p)\) be the smallest positive integer \(n\) which satisfies \(p \mid F_n\).
Miho Aoki, Yuho Sakai
openaire   +2 more sources

On Periodicity in Generalized Fibonacci Sequences

The American Mathematical Monthly, 1965
(1965). On Periodicity in Generalized Fibonacci Sequences. The American Mathematical Monthly: Vol. 72, No. 8, pp. 856-861.
openaire   +1 more source

A Generalized Fibonacci Sequence

The Fibonacci Quarterly, 1972
Fisher, P. S., Kohlbecker, E. E.
openaire   +2 more sources

Some Characteristics of Matrix Operators on Generalized Fibonacci Weighted Difference Sequence Space

Symmetry, 2022
Murat Candan
exaly  

An interesting generalized Fibonacci sequence: a two-by-two matrix representation

Afrika Matematika, 2020
Gamaliel Cerda-Morales
exaly  

On ∞-Generalized Fibonacci Sequences

The Fibonacci Quarterly, 1999
Walter Motta, Mustapha Rachidi, Osamu Saeki   +2 more
openaire   +1 more source

On the zero-multiplicity of the k-generalized Fibonacci sequence

Journal of Difference Equations and Applications, 2020
Jonathan Garcia, CARLOS A Gomez, Florian Luca   +2 more
exaly