A Novel Property of Generalized Fibonacci Sequence in Grids
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866908994490073088 |
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| author | Yang, Zixian Bai, Jianchao |
| author_facet | Yang, Zixian Bai, Jianchao |
| contents | Fibonacci sequence, generated by summing the preceding two terms, is a classical sequence renowned for its elegant properties. In this paper, leveraging properties of generalized Fibonacci sequences and formulas for consecutive sums of equidistant subsequences, we investigate the ratio of the sum of numbers along main-diagonal and sub-diagonal of odd-order grids containing generalized Fibonacci sequences. We show that this ratio is solely dependent on the order of the grid, providing a concise and splendid identity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05369 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Novel Property of Generalized Fibonacci Sequence in Grids Yang, Zixian Bai, Jianchao Combinatorics Fibonacci sequence, generated by summing the preceding two terms, is a classical sequence renowned for its elegant properties. In this paper, leveraging properties of generalized Fibonacci sequences and formulas for consecutive sums of equidistant subsequences, we investigate the ratio of the sum of numbers along main-diagonal and sub-diagonal of odd-order grids containing generalized Fibonacci sequences. We show that this ratio is solely dependent on the order of the grid, providing a concise and splendid identity. |
| title | A Novel Property of Generalized Fibonacci Sequence in Grids |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2407.05369 |