Coarse length can be unbounded in 3-step nilpotent Lie groups

In "On the asymptotics of the growth of 2-step nilpotent groups" (J. London Math. Soc. (2), 58 (1998) ), we remarked that, contrary to 2-step nilpotent simply connected Lie groups, in 3-step nilpotent simply connected Lie groups it is possible that `R-words' in the given generators cannot be replaced by an equally long R-word representing the same group element and having a bounded number of direction changes. In this note, we present an example for this phenomenon.