A closed formula for linear recurrences with constant coefficients
Fuente:
arXiv
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| Autori principali: | , , , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
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| _version_ | 1866911132413853696 |
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| author | Bruda, Glenn Fang, Bruce Gilman, Pico Marquez, Raul Miller, Steven J. Prapashtica, Beni Son, Daeyoung Waheed, Saad Wang, Janine |
| author_facet | Bruda, Glenn Fang, Bruce Gilman, Pico Marquez, Raul Miller, Steven J. Prapashtica, Beni Son, Daeyoung Waheed, Saad Wang, Janine |
| contents | Given a linear recurrence of the form $c_n=a_1c_{n-1}+\cdots+a_j c_{n-j}$, it is well-known that $c_n=\sum_{r}p_r(n)r^n$, where the sum is taken over the set of characteristic roots and each $p_r(n)$ is some polynomial. We give a closed formula for the coefficients of each polynomial $p_r(n)$ for any linear recurrence of this form. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_12660 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A closed formula for linear recurrences with constant coefficients Bruda, Glenn Fang, Bruce Gilman, Pico Marquez, Raul Miller, Steven J. Prapashtica, Beni Son, Daeyoung Waheed, Saad Wang, Janine Combinatorics 11B37, 11B39 Given a linear recurrence of the form $c_n=a_1c_{n-1}+\cdots+a_j c_{n-j}$, it is well-known that $c_n=\sum_{r}p_r(n)r^n$, where the sum is taken over the set of characteristic roots and each $p_r(n)$ is some polynomial. We give a closed formula for the coefficients of each polynomial $p_r(n)$ for any linear recurrence of this form. |
| title | A closed formula for linear recurrences with constant coefficients |
| topic | Combinatorics 11B37, 11B39 |
| url | https://arxiv.org/abs/2408.12660 |