What are the standard Pitru Tarpan mantras for direct ancestors?

According to the Manual of Hindu Funeral and Ancestral Rites, Pitru Tarpan for direct ancestors is performed using Pitru Tirtha (water offered through the space between thumb and index finger), facing South, with the sacred thread on the right shoulder (Apasavya). Three anjalis (handfuls) of water mixed with black sesame seeds are offered for each ancestor:

For the Father (Vasu form): Om Adya Asmatpita [Gotra] [Name] Sharma/Varma/Gupta Vasuswarupah Idam Satilam Gopuchchodakam Tasmai Svadha Namah

For the Grandfather (Rudra form): Om Adya Asmatpitamaha [Gotra] [Name] Sharma/Varma/Gupta Rudraswarupah Idam Satilam Gopuchchodakam Tasmai Svadha Namah

For the Great-grandfather (Aditya form): Om Adya Asmatprapitamaha [Gotra] [Name] Sharma/Varma/Gupta Adityaswarupah Idam Satilam Gopuchchodakam Tasmai Svadha Namah

For the Mother (Vasu form): Om Adya Asmanmata [Gotra] [Name] Devi Vasuswarupa Idam Satilam Gopuchchodakam Tasyai Svadha Namah

Replace [Gotra] with your family gotra and [Name] with the ancestor”s name. For Sharma/Varma/Gupta, use the appropriate varna suffix. Each ancestor form (Vasu for parents, Rudra for grandparents, Aditya for great-grandparents) reflects the scriptural understanding of their progression toward liberation.