The $n$th term of an automatic sequence is the output of a deterministic finite automaton fed with the representation of $n$ in a suitable numeration system. In this paper, instead of considering automatic sequences built on a numeration system with a regular numeration language, we consider those built on languages associated with trees having periodic labeled signatures and, in particular, rational base numeration systems. We obtain two main characterizations of these sequences. The first one is concerned with $r$-block substitutions where $r$ morphisms are applied periodically. In particular, we provide examples of such sequences that are not morphic. The second characterization involves the factors, or subtrees of finite height, of the tree associated with the numeration system and decorated by the terms of the sequence.

翻译：自动序列的第n美元术语是一个确定性的有限自动计量器的输出,在适当的计数系统中以一美元为代表。本文不考虑在带有定期计数语言的计数系统上建立的自动序列,而是考虑那些基于有定期标记签名的树木相关语言,特别是合理基数系统的语言。我们获得了这些序列的两个主要特征。第一个涉及美元区块替代,定期使用美元区块。特别是,我们提供了这些不形态序列的例子。第二个特征涉及与计数系统相关的因素,或定高的亚树,以及按序列条件标注的树木。