Strongly k-recursive sequences
CoRR(2024)
摘要
Drawing inspiration from a recent paper of Heuberger, Krenn, and Lipnik, we
define the class of strongly k-recursive sequences. We show that every
k-automatic sequence is strongly k-recursive, therefore k-recursive, and
discuss that the converse is not true.
We also show that the class of strongly k-recursive sequences is a proper
subclass of the class of k-regular sequences, and we present some explicit
examples. We then extend the proof techniques to answer the same question for
the class of k-recursive sequences.
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