  A Ducci sequence is a sequence of integer $n$-tuples obtained by iterating
the map \[ D : (a_1, a_2, \ldots, a_n) \mapsto
\big(|a_1-a_2|,|a_2-a_3|,\ldots,|a_n-a_1|\big). \] Such a sequence is
eventually periodic and we denote by $P(n)$ the maximal period of such
sequences for given $n$. We prove lower bounds for $P(n)$ by counting certain
partitions.
