The asymptotics of the summatory function of regular sequences—a class of sequences which is basically defined by matrix products depending on a digit expansion—has been studied extensively (and presented at AofA meetings). In many cases, the sequence itself fluctuates too much in order to admit a direct analysis and it is only the summatory function where an asymptotic analysis makes sense. In some cases, however, the sequence itself admits a precise asymptotic expansion, for example in the case of sequences related to divide and conquer algorithms. In this talk, sufficient conditions (based on the eigenspaces of the matrices involved) for regular sequences admitting a precise asymptotic analysis are presented.

This is joint work with Mario Kurnig.