Results 61 to 70 of about 1,163,753 (215)
Some properties and extended Binet’s formula for the class of bifurcating Fibonacci sequence
Ratio MathematicaOne of the generalizations of Fibonacci sequence is a -Fibonacci sequence, which is further generalized in several other ways, some by conserving the initial conditions and others by conserving the related recurrence relation.
Daksha Manojbhai Diwan +2 more
doaj +1 more source
Generalized Fibonacci Numbers and Blackwell's Renewal Theorem [PDF]
, 2010 We investigate a connection between generalized Fibonacci numbers and renewal theory for stochastic processes. Using Blackwell's renewal theorem we find an approximation to the generalized Fibonacci numbers. With the help of error estimates in the renewal theorem we figure out an explicit representation.
arxiv +1 more source
On the Generalized Gaussian Fibonacci Numbers and Horadam Hybrid Numbers: A Unified Approach
Axioms, 2022 In this paper, we consider an approach based on the elementary matrix theory. In other words, we take into account the generalized Gaussian Fibonacci numbers. In this context, we consider a general tridiagonal matrix family.
Fatih Yılmaz, Mustafa Özkan
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On Summing Formulas For Generalized Fibonacci and Gaussian Generalized Fibonacci Numbers
Advances in Research, 2019 In this paper, closed forms of the summation formulas for generalized Fibonacci and Gaussian generalized Fibonacci numbers are presented. Then, some previous results are recovered as particular cases of the present results.
Y. Soykan
semanticscholar +1 more source
A curious property of series involving terms of generalized sequences
International Journal of Mathematics and Mathematical Sciences, 2000 Here we are concerned with series involving generalized Fibonacci numbers Un (p,q) and generalized Lucas numbers Vn (p,q). The aim of this paper is to find triples (p,q,r) for which the series Un (p,q)/rn and Vn (p,q)/rn (for r running from 0 to ...
Odoardo Brugia, Piero Filipponi
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Identities relating six members of the Fibonacci family of sequences
Karpatsʹkì Matematičnì Publìkacìï, 2022 In this paper, we prove several identities each relating a sum of products of three terms coming from different members of the Fibonacci family of sequences with a comparable sum whose terms come from three other sequences.
R. Frontczak, T. Goy, M. Shattuck
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Generalized double Fibonomial numbers
Ratio Mathematica, 2021 From the beginning of 20th century, generalization of binomial coefficient has been deliberated broadly. One of the most famous generalized binomial coefficients are Fibonomial coefficients, obtained by substituting Fibonacci numbers in place of natural ...
Mansi Shah, Shah Devbhadra
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Irreducibility of generalized Fibonacci polynomials [PDF]
arXiv, 2022 A second order polynomial sequence is of Fibonacci-type $\mathcal{F}_{n}$ (Lucas-type $\mathcal{L}_{n}$) if its Binet formula has a structure similar to that for Fibonacci (Lucas) numbers. Under certain conditions these polynomials are irreducible if and only if $n$ is a prime number.
arxiv
Some identities for generalized Fibonacci and Lucas numbers
AKCE International Journal of Graphs and Combinatorics, 2020 In this paper we study one parameter generalization of the Fibonacci numbers, Lucas numbers which generalizes the Jacobsthal numbers, Jacobsthal–Lucas numbers simultaneously. We present some their properties and interpretations also in graphs.
Anetta Szynal-Liana +2 more
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Some properties of Fibonacci numbers, Fibonacci octonions and generalized Fibonacci-Lucas octonions [PDF]
arXiv, 2015 In this paper we determine some properties of Fibonacci octonions. Also, we introduce the generalized Fibonacci-Lucas octonions and we investigate some properties of these elements.
arxiv