The point is in the above lineage you shall find the descendants of Ikshwaku/Rama fought along side the Kauravas and while Bhima defeated Dirghayaghna, Abhimanyu killed Vrishdvala!
There are Sanskrit slokas which convey both the Stories of Rama and Krishna in a Single verse, in A Palindrome Format.
You read straight, you get Ramayana.
Read it in the reverse order, Krishna’s Life Story.
I am providing below the Raghava Yadaviyam by Venkathdhvari
That saintly king and ruler (king) of the Dravida Countries who was known by the name of Satyavrata, at the end of the last kalpa (before the Pralaya) .. received knowledge by service to The Purusha, he indeed was Vaivaswata Manu, the son of Vivaswan, his sons have been proclaimed as the kings, famous as the Ikshvakus.
I furnish the details of Lord Rama’s’ Dynasty, Ancestors and Descendants. Manu had many sons of whom 50 perished quarelling with one another. Ten sons survived, one of whom was Ikshvaku. The Brahma Purana (Chapters 7 and 8) provides details on Manu’s 10 sons and their descendents as follows  Ikshvaku Nriga Dhrishta – also called Rishta. He ruled over Dharstika.…… Continue reading Lord Rama’s Dynasty Ancestors, Descendants List