The number of ancestors you have doubles every generation, but the segments of ancestral genomes contributing to your genome increases arithmetically by 71 per generation. So by 8+ generations, it is likely that you have some ancestors who did not contribute to your genome. By 15+ generations back, this is almost a certainty. See figure below to watch this play out. The figure is borrowed from David Reich’s Who We Are And How We Got Here who adapted the data from a blog post by population geneticist Graham Coop.