Non-standard Zeckendorf decompositions; or, Tribonacci within Fibonacci
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913040508649472 |
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| author | Anders, Katie Dawsey, Madeline L. Vandehey, Joseph |
| author_facet | Anders, Katie Dawsey, Madeline L. Vandehey, Joseph |
| contents | We study $B(n;k)$, the number of ways of writing $n$ as a sum or difference of the first $k$ Fibonacci numbers. We show that $B(0;k)$ satisfies the Tribonacci-like recurrence $B(0;k+1)=B(0;k)+B(0;k-1)+B(0;k-2)$ and that $B(n;k)$ satisfies a modified version of this recurrence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_15446 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-standard Zeckendorf decompositions; or, Tribonacci within Fibonacci Anders, Katie Dawsey, Madeline L. Vandehey, Joseph Number Theory Combinatorics 11B37, 11B38, 11A63 We study $B(n;k)$, the number of ways of writing $n$ as a sum or difference of the first $k$ Fibonacci numbers. We show that $B(0;k)$ satisfies the Tribonacci-like recurrence $B(0;k+1)=B(0;k)+B(0;k-1)+B(0;k-2)$ and that $B(n;k)$ satisfies a modified version of this recurrence. |
| title | Non-standard Zeckendorf decompositions; or, Tribonacci within Fibonacci |
| topic | Number Theory Combinatorics 11B37, 11B38, 11A63 |
| url | https://arxiv.org/abs/2604.15446 |