First things first: Take the ethnicity mix you receive from the autosomal DNA tests with liberal grains of salt. The science behind the ethnicity estimates is developing, in a few years it may have reached the point where you can rely on it, but not yet.
Now, taking the above into account, the number of generations is very random. Two siblings each inherit 50% of their auDNA from each of their parents, who each received 50% from their parents, and so on back to the birth of humankind. The trick is, though, that each sibling's DNA inheritance is a random sampling from each of their parents (except for identical twins), and the parents got a random 50% from theirs, and so on.
Picture it this way; gather two sets of blocks, each numbered 1 - 100. One set is your father's DNA segments and the other is your mother's. Now take a 100 sided dice (good luck finding one of those!), roll it 50 times for your father's segments, and 50 for your mothers. Now for your sibling . . . roll the dice another 50 times for your sibling's father share and 50 times for his mother share. Compare your results with your siblings, you'll share some segments from each parent but not all. You get some differences with just 2 parents . . . now try and figure out how much of your 4 grandparents' DNA you received, and then how much your sibling received and how different his is from yours. It gets complicated. Go back to your 8 great grandparents, and it is even more complicated, and we are only at 3 generations.
Simple math and statistics tell us that by the time 5 or 6, maybe 7, generations go by the odds of receiving any DNA at all from a specific grandparent of that generation is low, and if you do beat the odds the amount you receive will most likely be pretty small. However, if both grandparents from that generation are 100% Native American or African, then the odds increase accordingly. Sill could be pretty small though.