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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.06512 |
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| _version_ | 1866915458523856896 |
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| author | Chua, Hongshen |
| author_facet | Chua, Hongshen |
| contents | This paper presents a reinterpretation of a second-order linear recurrence sequence as a sequence of continuants derived from the convergents to a continued fraction. As a result, we are able to derive the generating function and Binet formula for continuants. Using this result, we provide a continuant-based formulation for well-known identities associated with Lucas sequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06512 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Study of Second-Order Linear Recurrence Sequences via Continuants Chua, Hongshen Number Theory 11A55 (Primary), 11B39 (Secondary) This paper presents a reinterpretation of a second-order linear recurrence sequence as a sequence of continuants derived from the convergents to a continued fraction. As a result, we are able to derive the generating function and Binet formula for continuants. Using this result, we provide a continuant-based formulation for well-known identities associated with Lucas sequences. |
| title | A Study of Second-Order Linear Recurrence Sequences via Continuants |
| topic | Number Theory 11A55 (Primary), 11B39 (Secondary) |
| url | https://arxiv.org/abs/2501.06512 |