Results 31 to 40 of about 976 (217)
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 +1 more
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Solutions of equations x2−(p2q2±3p)y2=±kt
Examples and Counterexamples, 2022 In the present paper, we have solved the equation x2−(p2q2±3p)y2=kt,x2−(p2q2±5p)y2=ktand expressed its positive integer solutions in terms of generalized Fibonacci, generalized Lucas and generalized Pell, generalized Pell–Lucas sequences.
Roji Bala, Vinod Mishra
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Binomial Sum Relations Involving Fibonacci and Lucas Numbers
AppliedMath, 2023 In this paper, we provide a first systematic treatment of binomial sum relations involving (generalized) Fibonacci and Lucas numbers. The paper introduces various classes of relations involving (generalized) Fibonacci and Lucas numbers and different ...
Kunle Adegoke +2 more
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On the k-generalized Fibonacci numbers [PDF]
, 2012 In this paper, we define a new family of k-generalized Fibonacci numbers. Furthermore, we give sums and recurrence relations of this numbers and obtain generating functions of this numbers for k=2.
Yılmaz, Nazmiye +2 more
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Non-Fisherian generalized Fibonacci numbers [PDF]
Notes on Number Theory and Discrete MathematicsUsing biology as inspiration, this paper explores a generalization of the Fibonacci sequence that involves gender biased sexual reproduction. The female, male, and total population numbers along with their associated recurrence relations are considered ...
Thor Martinsen
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Square numbers, square pyramidal numbers, and generalized Fibonacci polynomials
Journal of New Results in Science, 2022 In this paper, we derive two interesting formulas for square and square pyramidal numbers. We focus on the linear recurrence relation with constant coefficients for square and square pyramidal numbers.
Adem Şahin
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On a generalization of dual-generalized complex Fibonacci quaternions [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this study, we introduce a new class of generalized quaternions whose components are dual-generalized complex Horadam numbers. We investigate some algebraic properties of them.
Elif Tan, Umut Öcal
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Generalized Fibonacci Numbers, Cosmological Analogies, and an Invariant [PDF]
Symmetry, 2021 Continuous generalizations of the Fibonacci sequence satisfy ODEs that are formal analogues of the Friedmann equation describing a spatially homogeneous and isotropic cosmology in general relativity. These analogies are presented together with their Lagrangian and Hamiltonian formulations and with an invariant of the Fibonacci sequence.
Valerio Faraoni, Farah Atieh
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Generalized Fibonacci Numbers and Music [PDF]
, 2018 Mathematics and music have well documented historical connections. Just as the ordinary Fibonacci numbers have links with the golden ratio, this paper considers generalized Fibonacci numbers developed from generalizations of the golden ratio.
Robert van Gend +5 more
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On Fibonacci (k,p)-Numbers and Their Interpretations
Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2023 In this paper, we define new kinds of Fibonacci numbers, which generalize both Fibonacci, Jacobsthal, Narayana numbers and Fibonacci p-numbers in the distance sense, using the definition of a distance between numbers by a recurrence relation according to
Berke Cengiz, Yasemin Taşyurdu
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