Find the direction in which to look for a solution

Question

Good time dear forum participants!

So, I just need an advice for direction, in which to look for a solution. For example, terminology in mathematics, or examples of similar problems.

I have 3 lists of values A, B and C

• A is a list of constants
• B is a list of variables
• C is a list of solutions

I also have a formula:

C(i) = B(i) - A(i) + C(i - 1)

where i is some iterator

https://i.stack.imgur.com/NClK4.jpg - here is a picture of A, B and C with 24 elements

It is to find such values of elements in list B so that the system meets the following requirements:

1. values in C can be in the range from 0 to 1000 strictly!
2. each element in list C can be up to 600 more or less than each previous element
3. each element in list B can be 100 more or less than each previous element
4. the order of the numbers in B should not have gaps in the form of 0 (or gaps should be as rare as possible)

It would be nice to find at least one solution (such as the one shown in the picture), or better yet, all possible solutions.

Thanks in advance for your ideas and tips!

I tried the method of building up values in list B in form of pyramids like 100, 200, 300, 400, 300, 200, 100 but it is not very convenient.

I also tried the regular prediction method for a few items ahead to make a decision. It's always a dead end.

The enumeration? it takes too long.

Machine learning? What else? matrices? differentials? What's the best?