I have an example of a DNA match across 3 generations and also a very good illustration of why the ability to compare in a chromosome browser is the only way to know with more certainty how we match someone. Below you see the match, Joy compared to my Mom,Beatrice. They share 10.1 cM across 1 DNA segment
Next let's look at my sister, Rebecca compared to Joy.(You can only do the comparison with tests for which you have admin or editor rights.) Looks like she didn't get that segment from Mom.
Compared with Joy she and I share 25.3 cMs across 2 segments. Wait--Mom only had 10.1 cM. Where did I pick up the other 15.2 cMs? Was it a no-call on Mom's test and actually from her side? Did I get it from my Dad? Dad passed before he could test but I have a phased kit of the DNA which I got from him. I could compare my paternal phased DNA if Joy were at GEDmatch. Hopefully she will upload her results there.
Now let's take a look at my daughter, Brittany compared to Joy. Looks like she got both segments and would have the potential for passing these segments on to any children she may have.
Thoughts: We can't know for sure that the 15.2 cM segment that I have and that I passed on is from my Dad without comparison of the tests results in a Chromosome Browser. Then we can draw some conclusions. Think about it though--Rebecca's two children will not have these segments because she did not have them to pass on to them. That is how sometimes we have different matches than our siblings DNA Randomness. It's no wonder that on average we only match about half of our 4th cousins.