What is the sankalpa mantra before beginning Pitru Tarpan?

The sankalpa (formal vow of intention) is recited at the beginning of Pitru Tarpan to formally commit to the ritual and to specify which ancestors are being honoured. The standard format includes your name, gotra, and the intention to satisfy the father, grandfather, and great-grandfather along with their wives:

Om Adya [Tithi] [Nakshatra] [Date] Asmat Pitri Pitamaha Prapitamaha Sapatnikanam Akshayatripti-sampadanartham Pitri Tarpanam Karishye

Translation: Today, on this [tithi] in the [nakshatra], I, [Name] of [Gotra], perform this Pitru Tarpan rite for my father, grandfather, and great-grandfather along with their wives, to grant them imperishable satisfaction.

Before reciting the sankalpa, the performer (Karta) takes a ritual purification bath (Snan), wears clean white clothes, holds the sacred thread (Yajnopavita) in the Apasavya position (right shoulder, left hip) for ancestral rituals, faces South, and holds water, sesame seeds, and darbha grass in his right hand while the sankalpa is recited by the officiating pandit.