I started to write a post last night…but realized I was way too tired to even attempt As you can see, there isn't really a simple answer. But I will try to sum up.
To have a tri puppy, you need to have either two tri parents (or a trindle - tri-brindle), or two parents who carry the recessive tri...could be any color, but the gene not expressed is a tri (meaning somewhere in their ancestry there was a tricolor)
To have a red puppy, pretty much any combination of basenjis (EXCEPT tri x tri) can make red puppies; though it is really rare to have reds from black x black breeding
To have a brindle puppy, you have to have a brindle parent; this could include trindle, or black/brindle (where the dog would LOOK black because you couldn't see the stripes, but would actually carry the brindle gene)
To have a black puppy, you have to have a black parent
So, to make it interesting, you could have a four color litter of pups with these parents: Tri-factored red (looks RED, carries tri gene) x Tri factored black brindle (looks BLACK, actually has "invisible" stripes, and carries tri gene)
I think...;) There are other combinations where you could get a four color litter as well, but this is the first one I thought of.
Does that help at all? It is confusing and likely to get more confusing as breeders are becoming more interested and tolerant of a whole host of other colors and patterns in which basenjis are found in Africa.
Many people don't realize there were originally creme colored basenjis, and fawn, and blue? Over the years, breeders have bred specifically for the three (now four) accepted colors, so the other colors were lost for the most part. I think the discussion of color is fascinating. With the African imports in the llate eighties, and now in the last few years, we are now really able to explore more about the natural coloration in Basenjis.