Hello Jim
First of all, let me just indicate that when Rene mentioned a “network” he is referring to a subnet of size /24, that is, with 256 host addresses (254 + network and broadcast). A network does not strictly need to be /24 as it can indeed be classless, however, for the purposes and constraints of this lesson and this topic, it is assumed that a “network” refers to a /24 subnet.
Now having said that, using your calculation would indeed result in the values that Rene has in his post. It is mathematically correct. However, I believe that Rene is simply listing the sizes of subnets in descending order, and just doubling the number of networks for each. It’s kind of like a “cheat sheet” that you can use for future reference.
You can continue the sequence by reducing the number of the slash prefix and doubling the number of networks all the way down to the /0 prefix if you like, and you’ll have all of the values necessary for any subnetting endeavor you may need, assuming you are sticking with /24 networks. Does that make sense?
I hope this has been helpful!
Laz