(All measurements refer to Outside Diameter, O.D.)
This is a variation of the Byzantine weave. I have found there are many ways to do this weave with different sizes of rings both 20 and 18 gauge. The tutorial shows how to work up this weave using all the same size of rings. I also have a couple variations at the bottom.

This is a sample of what this weave looks like. I used 18 gauge brass 6mm rings with a 7mm center ring.

First you need several Byzantine links, which you can find the tutorial for them HERE.

This is what 1 Byzantine link should look like.

To connect the links add 4 rings to your link as shown above. You can double these up if you want.

Now add your second link to the first as shown and continue until you have the desired length of your project.

This variation shows larger rings for the center rings, as in the sample above.

Some Variations

In this variation I used 2 rings for the connection rings. Then I added another ring in between those and only passed through the bottom 2 rings of the link. This connection is like a half Byzantine. 

In this sample I used 7mm 18g rings to make up the links with two 8mm rings in the center. Then I used 6mm 18g rings to make the half Byzantine connection. I also didn't like that it was rather loose and didn't hold its shape well. So, I connected the 8mm center rings with a 6mm ring and it worked perfectly.

This sample was made using all 5mm 20 gauge rings.  To add stability, I connected the center rings.

This sample was made using 5mm and 6mm 20 gauge rings. The connection is done with the half Byzantine and I added a size 6/0 seed bead.

As you can see, there is a lot of versatility with this weave. So, play around and have fun mixing sizes, colors.   Try adding some beads too.