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A Padovan-automatic description of a nested recurrence
We study the sequence $a(0)=0$, $a(1)=1$ and $a(n)=n-a(n-a(n-a(n-1)))$ for $n\ge 2$, listed as A076502 in the On-Line Encyclopedia of Integer Sequences. We identify $a(n)$ as a two-position shift in the greedy Padovan numeration system, with a finite-state correction. The proof constructs an additio
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