Cows explicit solution

[debtmaster]

I've solved the Cows problem explicitly. Steam can't format equations, so if you'd like to see the solution I've saved it on Desmos: https://www.desmos.com/calculator/4cmeix2ogq

The process was simple but the algebra was just overwhelming; it's otherwise solved like any other recursive linear equation. Considering this game's background I thought people might be interested :^)
(I've moved the post to this subforum)

[Kimossab]

the formula is much simpler:
f(x) = f(x-1) + f(x-3), x > 0
f(x) = 1, x = 0
f(x) = 0, x < 0

[debtmaster]

That's true, but it's implicit (i.e. the function references itself in its definition). If I asked you for f(255), using that you'd have to add values up to 255. If you solve that to get it explicity (get f(x) in terms of only x) you get what I've posted, and can just plug in f(255) to get the answer, which has 42 digits.