Coordination sequences of periodic structures are rational via automata theory.

The conjecture of Grosse-Kunstleve et al. [(1996), Acta Cryst. A52, 879-889], that coordination sequences of periodic structures in n-dimensional Euclidean space are rational, is proved. This has been recently proven by Nakamura et al. [(2021), Acta Cryst. A77, 138-148]; however, the proof presented here is a straightforward application of classic techniques from automata theory.