Is "Honor your children, and they will honor you" a Hadith or a saying of Omar, and to what extent is it Islamically authentic?

The aforementioned saying is not known to have been reported as a hadith from the Prophet, peace and blessings be upon him, nor from Umar, may Allah be pleased with him. A hadith related to this topic is: "Be dutiful to your fathers, and your children will be dutiful to you," but it is weak. It was narrated that Umar said to a father who mistreated his son: "You have been undutiful to him before he was undutiful to you," but we have not found a chain of narration for this. Perhaps this statement was made by one of the scholars or wise men, and its intention is that whoever raises his child well in childhood will reap his dutifulness in old age. This is generally true, but it is not a strict correlation; a parent may raise his child well, yet the child becomes undutiful, and a parent may raise his child poorly, yet the child becomes dutiful.