Some remarks on recursive sequence of fibonacci type
This paper presents a detailed procedure for determining the probability of return for random walks on $ \mathbb{Z} $, whose increment is given by a generalization of a well-known Fibonacci sequence, namely the $ k $-Fibonacci-like sequence $ (G_{k, n})_n $. Also, we study the size of the set of the...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2024-09-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://aimspress.com/article/doi/10.3934/math.20241262?viewType=HTML |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850264576296222720 |
|---|---|
| author | Najmeddine Attia |
| author_facet | Najmeddine Attia |
| author_sort | Najmeddine Attia |
| collection | DOAJ |
| description | This paper presents a detailed procedure for determining the probability of return for random walks on $ \mathbb{Z} $, whose increment is given by a generalization of a well-known Fibonacci sequence, namely the $ k $-Fibonacci-like sequence $ (G_{k, n})_n $. Also, we study the size of the set of these walks that return to the origin an infinite number of times, in term of fractal dimension. In addition, we investigate the limiting distribution of an adequate Markov chain that encapsulates the entire Tribonacci sequence $ ({\mathsf T}_n) $ to provide the limiting behavior of this sequence. |
| format | Article |
| id | doaj-art-0bf827cc1a1449daadbbafcc3df752ec |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-0bf827cc1a1449daadbbafcc3df752ec2025-08-20T01:54:40ZengAIMS PressAIMS Mathematics2473-69882024-09-0199258342584810.3934/math.20241262Some remarks on recursive sequence of fibonacci typeNajmeddine Attia 0Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsa 31982, Saudi ArabiaThis paper presents a detailed procedure for determining the probability of return for random walks on $ \mathbb{Z} $, whose increment is given by a generalization of a well-known Fibonacci sequence, namely the $ k $-Fibonacci-like sequence $ (G_{k, n})_n $. Also, we study the size of the set of these walks that return to the origin an infinite number of times, in term of fractal dimension. In addition, we investigate the limiting distribution of an adequate Markov chain that encapsulates the entire Tribonacci sequence $ ({\mathsf T}_n) $ to provide the limiting behavior of this sequence.https://aimspress.com/article/doi/10.3934/math.20241262?viewType=HTMLrandom walks$ k $-fibonacci like sequenceprobability of returnfractal dimensionmarkov chainbinet formula |
| spellingShingle | Najmeddine Attia Some remarks on recursive sequence of fibonacci type AIMS Mathematics random walks $ k $-fibonacci like sequence probability of return fractal dimension markov chain binet formula |
| title | Some remarks on recursive sequence of fibonacci type |
| title_full | Some remarks on recursive sequence of fibonacci type |
| title_fullStr | Some remarks on recursive sequence of fibonacci type |
| title_full_unstemmed | Some remarks on recursive sequence of fibonacci type |
| title_short | Some remarks on recursive sequence of fibonacci type |
| title_sort | some remarks on recursive sequence of fibonacci type |
| topic | random walks $ k $-fibonacci like sequence probability of return fractal dimension markov chain binet formula |
| url | https://aimspress.com/article/doi/10.3934/math.20241262?viewType=HTML |
| work_keys_str_mv | AT najmeddineattia someremarksonrecursivesequenceoffibonaccitype |