Q. (when celebrating the seuda on the third day after the bris) Is the day of the bris counted as day one?

A. From most Poskim it would seem that the day of the bris is day one. However, Horav Shlomo Miller Shlit’a mentioned that since some maintain (Bris Emes p. 303 quoting seforim, Al Pi Hatorah 9: 62) that this is a seudas hodoa, thanking Hashem for the newborn child and the bris performed, it would be more appropriate to celebrate the day after, when the newborn’s pain is already lessening. He suggested that if someone wants to celebrate this seuda, it should be better done after mincha, before sunset and prolonging after tzeis, followed by Ma’ariv.
Zechor L’Avrohom (p. 136) rules that if the bris took place on Thursday, this seuda is omitted, since the honor of Shabbos is that the seudos of Shabbos should belong to Shabbos itself.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a