Maciej Ulas

activity

20232026

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math.NT2024

Binary sequences meet the Fibonacci sequence

Piotr Miska, Bartosz Sobolewski, Maciej Ulas

We introduce a new family of meta-Fibonacci sequences $(f (n))_{n \in N}$ , governed by the recurrence relation $f (n) = a f (n - u_{n} - 1) + b f (n - u_{n} - 2),$ where $\mathbf{u}=(u_{n})…

math.NT2024

Signs behaviour of sums of weighted numbers of compositions

Filip Gawron, Maciej Ulas

Let $A$ be a subset of positive integers. For a given positive integer $n$ and $0 \leq i \leq n$ let $c_{A} (i, n)$ denotes the number of $A$ -compositions of $n$ with exactly $i$ parts…