Results 51 to 60 of about 1,240,285 (142)
On Sum Formulas for Generalized Tribonacci Sequence
, 2020 In this paper, closed forms of the sum formulas for generalized Tribonacci numbers are presented. As special cases, we give summation formulas of Tribonacci, Tribonacci-Lucas, Padovan, Perrin, Narayana and some other third-order linear recurrance ...
Yüksel Soykan
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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
wiley +1 more source
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
Identities involving the tribonacci numbers squared via tiling with combs [PDF]
, 2022 The number of ways to tile an $n$-board (an $n\times1$ rectangular board) with $(\frac12,\frac12;1)$-, $(\frac12,\frac12;2)$-, and $(\frac12,\frac12;3)$-combs is $T_{n+2}^2$ where $T_n$ is the $n$th tribonacci number.
Allen, Michael A., Edwards, Kenneth
core
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
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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On Some New Sequence Spaces and Their Duals
Journal of Mathematics, Volume 2024, Issue 1, 2024.In this study, we defined some new sequence spaces using regular Tribonacci matrix. We examined some properties of these spaces such as completeness, Schauder basis. We have identified α − , β−, and γ−duals of the newly created spaces.
Damla Barlak, Ömer Kişi
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A Study on Sum Formulas for Generalized Tribonacci Numbers: Closed Forms of the Sum Formulas ∑_{k=0}ⁿkx^{k}W_{k}, ∑_{k=1}ⁿkx^{k}W_{-k} [PDF]
, 2020 In this paper, closed forms of the sum formulas ∑_{k=0}ⁿkx^{k}W_{k}, ∑_{k=1}ⁿkx^{k}W_{-k} for generalized Tribonacci numbers are presented. As special cases, we give summation formulas of Tribonacci, Tribonacci-Lucas, Padovan, Perrin, Narayana and some ...
Soykan, Yüksel
core +2 more sources
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