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arXiv · 2501.14643

Complexity of powers of a constant-recursive sequence

Eric Rowland·Jesus Sistos Barron
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Abstract

Constant-recursive sequences are those which satisfy a linear recurrence, so that later terms can be obtained as a linear combination of the previous ones. The rank of a constant-recursive sequence is the minimal number of previous terms required for such a recurrence. For a constant-recursive sequence $s(n)$, we study the sequence $\left(\text{rank}\, s(n)^M\right)_{M\geq 1}$. We answer a question of Stinchcombe regarding the complexity of the powers of a constant-recursive sequence when the roots of the characteristic polynomial are not all distinct.

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Eric Rowland, Jesus Sistos Barron. 2025-01-24. Complexity of powers of a constant-recursive sequence. https://arxiv.org/abs/2501.14643

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