For every finitely generated virtually abelian group with any finite weighted generating set, geodesic growth is either polynomial with rational growth series or exponential with holonomic growth series, and the geodesic language is blind multicounter.
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Geodesic growth in virtually abelian groups
For every finitely generated virtually abelian group with any finite weighted generating set, geodesic growth is either polynomial with rational growth series or exponential with holonomic growth series, and the geodesic language is blind multicounter.