- The unmarked voice with the accusative - κατεκλίνεν τίνα with a valance of 2, meaning "(s)he lay sb. down" / "she caused sb. to recline".
- The subject-affected voice - ἀνεκλίθη with a valance of 1, meaning "(s)he sat down".
The BDAG entry, if you are comparing it, is delineated by what is caused to happen - lying or sitting. Presumably, the emphasis on the word "caused" is to accommodate the way that the meaning is constructed in the English idiom. That is to say that in English, we are quite happy to say, "She sat them down.", but we don't say, "She reclined them*."
I think that in Greek, it is what we see it here as - a strong (non-deleting) valence 2 (second element in the accusative) verb in the unmarked voice, and a valence 1 verb in the subject-affected voice. Besides the voice - valence interplay that this thread is asking about, his verb also requires a prepositional phrase indicating location, situation or whatever other condition that they were to recline in. Such a phrase is weak (subject to deletion, if it is clear from context).
I understand that valence is broadly defined category, but have I correctly counted the numbers. Should I be saying that the obligatory prepositional phrase is also a valence element? Am I right in identifying the similarity between this and the common English construction?