I think what you are trying to build is a Pseudo Random Generator PRG. I usually define them with the expansion property. The expansion means, that given a small amount of random numbers you can securely generate a bigger amount of random numbers.
Next we need to find your setup, what does an adversary see? If he only sees A to H I would assume the system is still secure and the numbers appear random to him. (In this case you don't have expansion) But if the adversary sees A1 to C2, I would not assume security. (In this case you have expansion)
The reason is quite simple. For security of a PRG the adversary is not allowed to distinguish the generated numbers from real random numbers with a probability greater than zero. But if you give him A1 to C2 and A to H he can just assume, that he archived it in this order (which happens with probability z). In that case he can check whether the given equations work out, which happens only with negligible probability for real random numbers, but with probability 1 in your example. Therefore with probability 0.5 (guessing) plus z he can distinguish both cases. Because z is not negligible, your PRG is not secure.
I tried to make the answer simplified without going into detail with all the math behind it, because your reputation seems low. If you want the more mathematical answer, just comment :D