Results 31 to 40 of about 2,369,502 (88)
On Sequences of Numbers and Polynomials Defined by Linear Recurrence Relations of Order 2
International Journal of Mathematics and Mathematical Sciences, Volume 2009, Issue 1, 2009., 2009 Here we present a new method to construct the explicit formula of a sequence of numbers and polynomials generated by a linear recurrence relation of order 2. The applications of the method to the Fibonacci and Lucas numbers, Chebyshev polynomials, the generalized Gegenbauer‐Humbert polynomials are also discussed.
Tian-Xiao He +2 more
wiley +1 more source
Twisted rational zeros of linear recurrence sequences
Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.Abstract We introduce the notion of a twisted rational zero of a nondegenerate linear recurrence sequence (LRS). We show that any nondegenerate LRS has only finitely many such twisted rational zeros. In the particular case of the Tribonacci sequence, we show that 1/3$1/3$ and −5/3$-5/3$ are the only twisted rational zeros that are not integral zeros.
Yuri Bilu +4 more
wiley +1 more source
On the Fibonacci Tiling and its Modern Ramifications
Israel Journal of Chemistry, Volume 64, Issue 10-11, November 2024.Abstract In the last 30 years, the mathematical theory of aperiodic order has developed enormously. Many new tilings and properties have been discovered, few of which are covered or anticipated by the early papers and books. Here, we start from the well‐known Fibonacci chain to explain some of them, with pointers to various generalisations as well as ...
Michael Baake +2 more
wiley +1 more source
International Journal of Mathematics and Mathematical Sciences, Volume 2024, Issue 1, 2024.Some boundedness and convergence properties of generalized Fibonacci’s‐type recurrences and their associated iterated recurrence ratios between pairs of consecutive terms are discussed under a wide number of initial conditions. Also, a more general, so‐called (k, q) Fibonacci’s recurrence and the associated Fibonacci’s ratio recurrences are ...
Manuel De la Sen, V. Ravichandran
wiley +1 more source
Binomial tribonacci sums [PDF]
Discrete Mathematics Letters, 2021 Kunle Adegoke +2 more
doaj +1 more source
Common terms of Tribonacci and Perrin sequences [PDF]
, 2022 Assume that T-n is the n(th) term of Tribonacci sequence and R-m is the m(th) term of Perrin sequence.
Irmak, Nurettin +4 more
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ON GENERALIZED TRIBONACCI SEDENIONS
, 2020 The sedenions form a 16-dimensional Cayley-Dickson algebra. In this work, we introduce the generalized Tribonacci sedenion and present someproperties of this sedenion.
Okumuş, İnci +2 more
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A Closed Formula for the Sums of Squares of Generalized Tribonacci numbers [PDF]
, 2020 In this paper, closed forms of the sum formulas for the squares of generalized Tribonacci numbers are presented. As special cases, we give summation formulas of the squares of Tribonacci, Tribonacci-Lucas, Padovan, Perrin, Narayana and some other third ...
Soykan, Yüksel
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Examination of generalized Tribonacci dual quaternions [PDF]
, 2023 This manuscript deals with introducing and discussing of a new type dual quaternions which are named generalized Tribonacci dual quaternions (GTDQ, for short).
İŞBİLİR, Zehra +2 more
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Unrestricted Tribonacci and Tribonacci–Lucas quaternions [PDF]
, 2023 We define a generalization of Tribonacci and Tribonacci-Lucas quaternions with arbitrary Tribonacci numbers and Tribonacci-Lucas numbers coefficients, respectively. We get generating functions and Binet's formulas for these quaternions.
Gonca Kızılaslan +3 more
core +2 more sources