Does a childrens ticket entitle the child to a seat/sleeper?

I have received ambiguous information about childrens tickets. I understand that free travel for children under 120cm does NOT entitle them to a seat/sleeper. I am not certain if the discounted ticket for children between 120-150cm entitles them to a seat/sleeper. Please confirm if I need to purchase an adult ticket to ensure a seat/sleeper for the child. thank you