Results 31 to 40 of about 123 (113)
On the Two‐Term Zeckendorf Representations of the Padovan and Perrin Sequences
Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.In this paper, we completely solve the Diophantine equations Pm = Fn + Fk and Em = Fn + Fk under the condition n ≥ k + 2 ≥ 4, where Pm is the m‐th Padovan number, Em is the m‐th Perrin number, and Fk is the k‐th Fibonacci number. This work determines all terms of the Padovan and Perrin sequences that admit a unique two‐term Zeckendorf representation ...
Awaou Lare Ousseni +4 more
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Binomial tribonacci sums [PDF]
Discrete Mathematics Letters, 2021 Kunle Adegoke +2 more
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A Hybrid Matrix–Based Encoding Scheme With Error Detection via Third‐Order Recurrences
Journal of Mathematics, Volume 2026, Issue 1, 2026.In this paper, we propose a novel encoding–decoding algorithm based on third‐order linear recurrence sequences and their associated matrix representations. In particular, third‐order Jacobsthal and third‐order Jacobsthal–Lucas matrix sequences are combined with Padovan and Perrin matrix sequences to construct a hybrid block–based coding scheme.
Sukran Uygun, Smritijit Sen
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Integer Semigroups Associated with Dumont‐Thomas Numeration Systems
International Scholarly Research Notices, Volume 2014, Issue 1, 2014., 2014 Given a primitive substitution, we define different binary operations on infinite subsets of the nonnegative integers. These binary operations are defined with the help of the Dumont‐Thomas numeration system; that is, a numeration system associated with the substitution. We give conditions for these semigroups to have an identity element.
Víctor F. Sirvent +5 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
k‐Step Sum and m‐Step Gap Fibonacci Sequence
International Scholarly Research Notices, Volume 2014, Issue 1, 2014., 2014 For two given integers k, m, we introduce the k‐step sumand m‐step gap Fibonacci sequence by presenting a recurrence formula that generates the nth term as the sum of k successive previous terms starting the sum at the mth previous term. Known sequences, like Fibonacci, tribonacci, tetranacci, and Padovan sequences, are derived for specific values of k,
Maria Adam +4 more
wiley +1 more source
Summing Formulas for Generalized Tribonacci Numbers
Universal Journal of Mathematics and Applications, 2020 In this paper, closed forms of the summation formulas for generalized Tribonacci numbers are presented. Then, some previous results are recovered as particular cases of the present results. As special cases, we give summation formulas of Tribonacci, Tribonacci-Lucas, Padovan, Perrin, Narayana and some other third order linear recurrance sequences.
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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
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Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014 Circulant matrices play an important role in solving ordinary and partial differential equations. In this paper, by using the inverse factorization of polynomial of degree n, the explicit determinants of circulant and left circulant matrix involving Tribonacci numbers or generalized Lucas numbers are expressed in terms of Tribonacci numbers and ...
Juan Li +3 more
wiley +1 more source
On perfect numbers close to Tribonacci numbers
AIP Conference Proceedings, 2018 In [1], Faco and Marques gave the conditions that even perfect numbers belonging to k-generalized Fibonacci numbers. In this paper, we present alternative proof for being even perfect numbers in Tribonacci sequence. Our methods depends on p-adic order of a Tribonacci number. Moreover, we present the perfect numbers with distance 1 to Tribonacci numbers.
Irmak, Nurettin, Acikel, Abdullah
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