So lemme work this out. Assuming just one Native American ancestor, the breakdown by generation is
Generation
offset:
---------
1 . . . . . . . Parent --> 1/2
2 . . . . . . . Grandparent --> 1/4
3 . . . . . . . Great-grandparent --> 1/8
4 . . . . . . . Great-great-grandparent --> 1/16
5 . . . . . . . Great-great-great grandparent --> 1/32
6 . . . . . . . Great-great-great-great grandparent --> 1/64
7 . . . . . . . Great-great-great-great-great grandparent --> 1/32
8 . . . . . . . Great-great-great-great-great-great grandparent --> 1/64
And this is assuming that the one Native American ancestor was a 100 percent Native American, not a mix him/herself. According to a woman I worked with many years ago, who was an enrolled member of a Western tribe, each tribe decide how much tribal blood you have to have to be eligible for enrollment. She said her tribe (Flatheads) was 1/16, but that most are 1/8.