Non-standard Zeckendorf decompositions; or, Tribonacci within Fibonacci
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.
Authors
- Katie Anders (ORCID: https://orcid.org/0000-0001-8424-9062)
- Joseph Vandehey
- Madeline L. Dawsey
Institutions
- The University of Texas at Tyler (US)
Publication Details
- Journal
- The Fibonacci Quarterly
- Published
- 2026-08-03
- DOI
- https://doi.org/10.1080/00150517.2026.2676035
- Primary Topic
- Advanced Mathematical Theories and Applications
- Type
- article
- Field-Weighted Citation Impact
- 0.00