Слова в линейных группах, случайные блуждания, автоматы, и P-рекурсивность

Fix a finite set $S \subset GL(k,Z)$ and denote by $an$ the number of products of matrices in $S$ of length $n$ that are equal to 1. We show that the sequence $\{an\}$ is not always P-recursive. This answers a question of Kontsevich.