Results 81 to 90 of about 3,822 (183)
On repdigits as product of $k$-Fibonacci and $k$-Lucas numbers [PDF]
Mathematica BohemicaFor an integer $k\geq2$, let $(F_n^{(k)})_{n\geq-(k-2)}$, $(L_n^{(k)})_{n \geq-(k-2)}$ be $k$-Fibonacci and $k$-Lucas sequences, respectively. For these sequences the first $k$ terms are $0,\ldots,0,1$ and $0,\ldots,0,2,1$, respectively, and each term ...
Safia Seffah +2 more
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Journal of Mathematics, Volume 2024, Issue 1, 2024.One important algebraic invariant in networks is complexity. This invariant ensures the accuracy and dependability of the network. In this paper, we employ a combinatorial approach to determine the graph’s complexity. A fundamental set of building blocks (basic graphs) will serve as the foundation for all the graphs we investigate, after which we will ...
Mohamed R. Zeen El Deen +3 more
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On the Leonardo Sequence via Pascal‐Type Triangles
Journal of Mathematics, Volume 2024, Issue 1, 2024.In this study, we discussed the Leonardo number sequence, which has been studied recently and caught more attention. We used Pascal and Hosoya‐like triangles to make it easier to examine the basic properties of these numbers. With the help of the properties obtained in this study, we defined a number sequence containing the new type of Leonardo numbers
Serpil Halıcı +2 more
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Determinant Representations of Sequences: A Survey
Special Matrices, 2014 This is a survey of recent results concerning (integer) matrices whose leading principal minors are well-known sequences such as Fibonacci, Lucas, Jacobsthal and Pell (sub)sequences. There are different ways for constructing such matrices.
Moghaddamfar A. R. +2 more
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An algorithm for complex factorization of the bi-periodic Fibonacci and Lucas polynomials [PDF]
Notes on Number Theory and Discrete MathematicsIn this paper, we consider the factorization of generalized sequences, by employing a method based on trigonometric identities. The new method is of reduced complexity and represents an improvement compared to existing results.
Baijuan Shi, Can Kızılateş
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Some basic properties of the generalized bi-periodic Fibonacci and Lucas sequences
Advances in Difference Equations, 2020 In this paper, we consider a generalization of Horadam sequence {wn} $\{ w_{n} \} $ which is defined by the recurrence relation wn=χ(n)wn−1+cwn−2 $w_{n}=\chi ( n ) w_{n-1}+cw_{n-2}$, where χ(n)=a $\chi ( n ) =a$ if n is even, χ(n)=b $\chi ( n ) =b$ if n ...
Elif Tan, Ho-Hon Leung
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Construction of helices from Lucas and Fibonacci sequences
, 2017 By means of two complex-valued functions (depending on an integer parameter P>=1) we construct helices of integer ratio R>=1 related to the so-called Binet formulae for P-Lucas and P-Fibonacci sequences. Based on these functions a new map is defined and we show that its three-dimensional representation is also a helix.
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The sequences of Fibonacci and Lucas for quadratic fields
Boletim da Sociedade Paranaense de MatemáticaWe construct the sequences of Fibonacci and Lucas in any quadratic field $\mathbb{Q}(\sqrt{d}\,)$ with $d>0$ square free, noting that the general properties remain valid as those given by the classical sequences of Fibonacci and Lucas for the case $d = 5$, under the respective variants.
Pablo Lam-Estrada +5 more
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The bi-periodic Horadam sequence and some perturbed tridiagonal 2-Toeplitz matrices: A unified approach. [PDF]
Heliyon, 2022 Anđelić M, da Fonseca CM, Yılmaz F.
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A Note on Stability of an Operator Linear Equation of the Second Order
Abstract and Applied Analysis, 2011 We prove some Hyers-Ulam stability results for an operator linear equation of the second order that is patterned on the difference equation, which defines the Lucas sequences (and in particular the Fibonacci numbers).
Janusz Brzdȩk, Soon-Mo Jung
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