Server architecture provides you with a lot of flexibility in how you choose to deploy. The documentation doesn't really call this out specifically.
The key things I'd recommend you keep in mind:
1. Minimum hardware recommendations. Installing a full fledged server (all processes) is not supported on machines with less than 4 cores. The installer will not continue if it detects in sufficient resources.
2. When installing a server on a 4 core machine, depending on the RAM/Disk available,by design, the server will install "fewer" server processes than when installing on recommended hardware for production/load use. Such a deployment is not ideal for load/product setup. Its fine for prototyping and trails.
3. You can, in some situations, separate out the backgrounder on it's own worker node on a 4 core machine with sufficient RAM/Disk such that (this should not share any other CPU or other resource intensive server process).
4. Consider licensing because you should make sure you have the right set of license keys so you can maximize your infrastructure use. Talk to your sales person about this.
5. Some server process are CPU bound - like vizql, background, data engine etc. The online docs, provide guidance on when to increase server process count.
Hope this is helpful. Without knowing your specific situation, I cannot recommend a mix
If you need help, reach out to your Tableau team for your account and they can find what makes the most sense in your situation.
In most situations Tableau seems to offer better performance going for 2 machines with 8+8 cores, with the Backgrounders separated.
Only reason I can think of to split 16 cores into 3 machines would be if you absolutely must have high availability.
In this particular example, each machine has 16 cores (rather than 16 cores spread across all three):
"In this example, all machines are assumed to be 64-bit, 16 core, 16+ GB systems.
- Run 2 VizQL server processes, 2 cache server processes, and 2 data server processes on the nodes that are not running the background processes. These are the recommended defaults from installation.
- As a general rule, run a cache server process for every VizQL server process.
- For this configuration, 16 cores are recommended for each node."
You could achieve the same with 3 8-core machines, but that environment would support less users than one with 16 cores per computer. Tableau Server configurations are highly flexible depending on your unique use case. I'd reach out to your Account Manager to talk about exactly what you need to get the most out of your Tableau Server installation.