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On escape criterion of an orbit with s-convexity and illustrations of the behavior shifts in Mandelbrot and Julia set fractals. [PDF]
Alam KH +4 more
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k-generalized Fibonacci numbers of the form 1+2^{n_1}+4^{n_2}+\cdots+(2^{k})^{n_k}
Carlos A. Gómez, Florian Luca
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Ratios of Generalized Fibonacci Numbers
The Fibonacci Quarterly, 2022A. Beardon
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On a Solvable System of Difference Equations in Terms of Generalized Fibonacci Numbers
Mathematica Slovaca, 2023In this paper, we represent that the following three-dimensional system of difference equations xn+1=αyn+aynyn−βzn−1, yn+1=βzn+bznzn−γxn−1, zn+1=γxn+cxnxn−αyn−1, n∈ℕ0, $$\matrix{{{x_{n + 1}} = \alpha {y_n} + {{a{y_n}} \over {{y_n} - \beta {z_{n - 1}}}},\
A. Yüksel, Y. Yazlık
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On the alternating sums of reciprocal generalized Fibonacci numbers
, 2021In this paper, we consider finite alternating sums derived from the generalized Fibonacci numbers [Formula: see text] [Formula: see text] and [Formula: see text], where [Formula: see text] and [Formula: see text] are positive integers with [Formula: see ...
Y. T. Ulutas, Gökhan Kuzuoğlu
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Generalized Hyper-Fibonacci Numbers and Applications
2022\textit{Hyper-Fibonacci numbers} were first defined by \textit{A. Dil} and \textit{I. Mező} [Appl. Math. Comput. 206, No. 2, 942--951 (2008; Zbl 1200.65104)]. The goal of the paper under review is to (i) provide some combinatorial properties of a generalization of the \textit{hyper-Fibonacci numbers}, and (ii) to apply these properties to the \textit ...
Ait-Amrane, Lyes, Behloul, Djilali
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Triangular numbers and generalized fibonacci polynomial
Mathematica Slovaca, 2022AbstractIn the present paper, we study triangular numbers. We focus on the linear homogeneous recurrence relation of degree 3 with constant coefficients for triangular numbers. Then we deal with the relationship between generalized Fibonacci polynomials and triangular numbers.
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