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The mathematics of generalized Fibonacci sequences: Binet's formula and identities [PDF]

Mathematica Moravica
This article considers a generalized Fibonacci sequence {Vn} with general initial conditions, V0 = a, V1 = b, and a versatile recurrence relation Vn = pVn-1 + qVn-2, where n ≥ 2 and a, b, p and q are any non-zero real numbers. The generating function and
Verma K.L.
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The Horadam Hybrid Numbers

Discussiones Mathematicae - General Algebra and Applications, 2018
In this paper we introduce the Horadam hybrid numbers and give some their properties: Binet formula, character and generating function.
Szynal-Liana Anetta
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On Hybrid Hyper k-Pell, k-Pell–Lucas, and Modified k-Pell Numbers

Axioms, 2023
Many different number systems have been the topic of research. One of the recently studied number systems is that of hybrid numbers, which are generalizations of other number systems.
Elen Viviani Pereira Spreafico, Paula Catarino, Paulo Vasco   +2 more
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On the Bicomplex Generalized Tribonacci Quaternions

Mathematics, 2019
In this paper, we introduce the bicomplex generalized tribonacci quaternions. Furthermore, Binet’s formula, generating functions, and the summation formula for this type of quaternion are given. Lastly, as an application, we present the determinant
Can Kızılateş, Paula Catarino, Naim Tuğlu   +2 more
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Optical properties of null geodesics emerging from dynamical systems

European Physical Journal C: Particles and Fields, 2022
We study optical metrics via null geodesics as a central force system, deduce the related Binet equation and apply the analysis to certain solutions of Einstein’s equations with and without spherical symmetry.
D. Batic, S. Chanda, P. Guha
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The sequence of trifurcating Fibonacci numbers

Ratio Mathematica, 2021
One of the interesting generalizations of Fibonacci sequence is a k-Fibonacci sequence, which is further generalized into the ‘Bifurcating Fibonacci sequence’.
Parimalkumar A. Patel, Dr. Devbhadra V. Shah   +1 more
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A Context-Free Grammar Associated with Fibonacci and Lucas Sequences

Journal of Mathematics, 2023
We introduce a context-free grammar G=s⟶s+d,d⟶s to generate Fibonacci and Lucas sequences. By applying the grammar G, we give a grammatical proof of the Binet formula.
Harold Ruilong Yang
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Fractional Statistics in terms of the r-Generalized Fibonacci Sequences [PDF]

, 2001
We develop the basis of the two dimensional generalized quantum statistical systems by using results on $r$-generalized Fibonacci sequences. According to the spin value $s$ of the 2d-quasiparticles, we distinguish four classes of quantum statistical ...
E. H. SAIDI, Haldane F. D. H., J. ZEROUAOUI, Laughlin R. B., M. RACHIDI, Rachidi M., Wu Y. S.   +6 more
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Theory of Binet formulas for Fibonacci and Lucas p-numbers

Chaos, Solitons & Fractals, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Stakhov, Alexey, Rozin, Boris
  +9 more sources

Binomial transform of the bivariate Fibonacci quaternion polynomials and its properties [PDF]

Notes on Number Theory and Discrete Mathematics
The primary aim of this work is to deal with binomial transforms of bivariate Fibonacci quaternion polynomial sequence. The binomial sequence of the bivariate Fibonacci quaternion polynomial is found, and then results are obtained for the recurrence ...
Faruk Kaplan, Arzu Özkoç Öztürk
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