Sequences of numbers (either natural integers, or integers or rational) of level $k \in \mathbb{N}$ have been defined in \cite{Fra05,Fra-Sen06} as the sequences which can be computed by deterministic pushdown automata of level $k$. This definition has been extended to sequences of {\em words} indexed by {\em words} in \cite{Sen07,Fer-Mar-Sen14}. We characterise here the sequences of level 3 as the compositions of two HDT0L-systems. Two applications are derived: - the sequences of rational numbers of level 3 are characterised by polynomial recurrences - the equality problem for sequences of rational numbers of level 3 is decidable.

翻译：序列（自然整数、整数或有理数）中级别为$k \in \mathbb{N}$的序列在文献\cite{Fra05,Fra-Sen06}中被定义为可由级别$k$的确定性下推自动机计算的序列。该定义在文献\cite{Sen07,Fer-Mar-Sen14}中被扩展为以{\em 词}索引的{\em 词}序列。本文刻画了级别3的序列作为两个HDT0L系统的复合。由此得出两个应用：- 级别3的有理数序列可通过多项式递归刻画；- 级别3的有理数序列的相等性问题是可判定的。