### On the growth of groups and automorphisms

#### To appear in IJAC volume in honour of R.Grigorchuk

We consider the growth functions $\beta_\G(n)$ of amalgamated free products $\G=A\ast_C B$, where $A\cong B$ are finitely generated, $C$ is free abelian and $|A/C|=|A/B|=2$. For every $d\in\mathbb N$ there exist examples with $\beta_\G(n)\simeq n^{d+1}\beta_A(n)$. There also exist examples with $\beta_\Gamma(n)\simeq e^n$. Similar behaviour is exhibited among Dehn functions.