Results 61 to 70 of about 48,003 (223)

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

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

Sequences of Numbers Meet the Generalized Gegenbauer-Humbert Polynomials [PDF]

, 2011
Here we present a connection between a sequence of numbers generated by a linear recurrence relation of order 2 and sequences of the generalized Gegenbauer-Humbert polynomials.
Peter J.-S. Shiue, Tian-Xiao He, Tsui-Wei Weng   +2 more
core   +2 more sources

On Generalized Fibonacci Numbers [PDF]

The American Mathematical Monthly, 1971
(1971). On Generalized Fibonacci Numbers. The American Mathematical Monthly: Vol. 78, No. 10, pp. 1108-1109.
openaire   +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,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 the bounds for the spectral norms of geometric circulant matrices

Journal of Inequalities and Applications, 2016
In this paper, we define a geometric circulant matrix whose entries are the generalized Fibonacci numbers and hyperharmonic Fibonacci numbers. Then we give upper and lower bounds for the spectral norms of these matrices.
Can Kızılateş, Naim Tuglu
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 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

The asymptotic behavior of the reciprocal sum of generalized Fibonacci numbers

Electronic Research Archive
Let $ \left(u_n\right)_{n\geq0} $ be the special Lucas $ u $-sequence defined by \begin{document}$ u_{n+2} = Au_{n+1}-Bu_n,\quad u_0 = 0,\, u_1 = 1, $\end{document} where $ n\geq0 $, $ B = \pm1 $, and $ A $ is an integer such that $ A^2-4B > 0 $. Let
Hongjian Li, Kaili Yang, Pingzhi Yuan
semanticscholar   +1 more source