Find a function that respect these 3 conditions

Question

I am developing a mobile app to help to memorize by heart and review a book and I don't know how to solve this math problem.
I have a function f which is a quadratic function representing the total number of memorized lines up to now (so f ' is the number of new memorized lines for the day).
I'm looking for function g which is the number of lines to be revised per day knowing that

1. the book has "l" lines
2. 1. first, each new line memorized must be reviewed every day for "a" days
   2. then (after "a" days), the line must be reviewed once every "b" days.
3. "b" is a variable starting at "c" and incrementing by 1 at each revision until reaching "d".

I did calculus 1 & 2 and discrete math. Thanks

If the question is too difficult, I could define a, c and d and also give the function f

link to the same question on mathematics subreddit: https://www.reddit.com/r/mathematics/comments/ifbjbw/find_the_function_that_respect_these_3_conditions/

link to the same question on casual math subreddit (1 answer with algorithm): https://www.reddit.com/r/CasualMath/comments/ifbvvp/find_the_function_that_respect_these_3_conditions/?utm_source=share&utm_medium=web2x&context=3

EDIT : I used an algorithm to solve my problem

Answer 1

Here's an attempt:$$g(t)=\sum_{n=1}^{a}f'(t-n)$$This formula only satisfies the first condition though. After this I get completely stuck. You would arrive at a system of difference equations with d members. Even with c and d given, this seems near futile.

But, since you're coding, you don't have to find a formula, there's a much simpler solution, but that's off topic for this website. If you want my advice on a coding solution to this problem, let me know in the comments, but I'm not sure how to solve your math problem.