  The coordination sequence s(k) of a graph counts the number of its vertices
which have distance k from a given vertex, where the distance between two
vertices is defined as the minimal number of bonds in any path connecting them.
For a large class of graphs, including in particular the classical root
lattices, we present the coordination sequences and their generating functions,
summarizing and extending recent results of Conway and Sloane. A possible
application to the theory of critical phenomena in lattice models is outlined.
