K. Anders

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math.NT2026

Non-standard Zeckendorf decompositions; or, Tribonacci within Fibonacci

Katie Anders, Madeline L. Dawsey, Joseph Vandehey

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;…

math.NT2025

Non-standard quaternary representations and the Fibonacci numbers

Katie Anders, Madeline L. Dawsey, Rajat Gupta +2

Let $f_{4} (n)$ be the number of hyperquaternary representations of $n$ and $b_{4} (n)$ be the number of balanced quaternary representations of $n$ . We show that there is no integer $k$ …