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Fix a finite set $S \subset {GL}(k,\mathbb{Z})$. Denote by $a_n$ the numberof products of matrices in $S$ of length $n$ that are equal to 1. We show thatthe sequence $\{a_n\}$ is not always P-recursive. This answers a question ofKontsevich.

Words in Linear Groups, Random Walks, Automata and P-Recursiveness