Results 31 to 40 of about 973 (216)

GENERALIZED FIBONACCI NUMBERS AND DIMER STATISTICS [PDF]

Modern Physics Letters B, 2002
We establish new product identities involving the q-analogue of the Fibonacci numbers. We show that the identities lead to alternate expressions of generating functions for close-packed dimers on non-orientable surfaces.
Lu, W. T., Wu, F. Y.
openaire   +3 more sources

On the sequences of $(q,k)$-generalized Fibonacci numbers [PDF]

Mathematica Bohemica
We consider a new family of recurrence sequences, the $(q,k)$-generalized Fibonacci numbers. These sequences naturally extend the well-known sequences of $k$-generalized Fibonacci numbers and generalized $k$-order Pell numbers.
Jean Lelis, Gersica Freitas, Alessandra Kreutz, Elaine Silva   +3 more
doaj   +1 more source

Almost Repdigit k-Fibonacci Numbers with an Application of k-Generalized Fibonacci Sequences

Mathematics, 2023
In this paper, we define the notion of almost repdigit as a positive integer whose digits are all equal except for at most one digit, and we search all terms of the k-generalized Fibonacci sequence which are almost repdigits. In particular, we find all k-
Alaa Altassan, Murat Alan
doaj   +1 more source

An Alternating Sum of Fibonacci and Lucas Numbers of Order k

Mathematics, 2020
During the last decade, many researchers have focused on proving identities that reveal the relation between Fibonacci and Lucas numbers. Very recently, one of these identities has been generalized to the case of Fibonacci and Lucas numbers of order k ...
Spiros D. Dafnis, Andreas N. Philippou, Ioannis E. Livieris   +2 more
doaj   +1 more source

On generalized bicomplex k-Fibonacci numbers [PDF]

, 2019
In this paper, we introduce the generalized bicomplex k-Fibonacci numbers. We also give the generating function and Binet's formula for these numbers.
Yağmur, Tülay
core   +1 more source

Incomplete Bivariate Fibonacci and Lucas 𝑝-Polynomials

Discrete Dynamics in Nature and Society, 2012
We define the incomplete bivariate Fibonacci and Lucas 𝑝-polynomials. In the case 𝑥=1, 𝑦=1, we obtain the incomplete Fibonacci and Lucas 𝑝-numbers. If 𝑥=2, 𝑦=1, we have the incomplete Pell and Pell-Lucas 𝑝-numbers.
Dursun Tasci, Mirac Cetin Firengiz, Naim Tuglu   +2 more
doaj   +1 more source

Bernoulli F-polynomials and Fibo–Bernoulli matrices

Advances in Difference Equations, 2019
In this article, we define the Euler–Fibonacci numbers, polynomials and their exponential generating function. Several relations are established involving the Bernoulli F-polynomials, the Euler–Fibonacci numbers and the Euler–Fibonacci polynomials. A new
Semra Kuş, Naim Tuglu, Taekyun Kim
doaj   +1 more source

On $k$-Fibonacci balancing and $k$-Fibonacci Lucas-balancing numbers

Karpatsʹkì Matematičnì Publìkacìï, 2021
The balancing number $n$ and the balancer $r$ are solution of the Diophantine equation $$1+2+\cdots+(n-1) = (n+1)+(n+2)+\cdots+(n+r). $$ It is well known that if $n$ is balancing number, then $8n^2 + 1$ is a perfect square and its positive square root is
S.E. Rihane
doaj   +1 more source

On (k,p)-Fibonacci numbers and matrices [PDF]

Notes on Number Theory and Discrete Mathematics
In this paper, some relations between the powers of any matrices X satisfying the equation Xᵏ-pXᵏ⁻¹-(p-1)X-I=0 and (k,p)-Fibonacci numbers are established with ...
Sinan Karakaya, Halim Özdemir, Tuğba Demirkol   +2 more
doaj   +1 more source

On Generalized Jacobsthal and Jacobsthal–Lucas Numbers

Annales Mathematicae Silesianae, 2022
Jacobsthal numbers and Jacobsthal–Lucas numbers are some of the most studied special integer sequences related to the Fibonacci numbers. In this study, we introduce one parameter generalizations of Jacobsthal numbers and Jacobsthal–Lucas numbers.
Bród Dorota, Michalski Adrian
doaj   +1 more source