We show that any subgroup of a finitely generated virtually abelian group grows rationally relative to , that the set of right cosets of any subgroup of grows rationally, and that the set of conjugacy classes of grows rationally. These results hold regardless of the choice of finite weighted generating set for .
Alex Evetts. "Rational growth in virtually abelian groups." Illinois J. Math. 63 (4) 513 - 549, December 2019. https://doi.org/10.1215/00192082-8011497