What is Player Agency?

[jayem]

That is a great analogy.

And taken from there when you have the formula, not only can you extent it onwards, but if you can get a general form you can also theoretically fill in the gaps.
I don't know if there's any use for the Fibs (other than finding that after 19.37 years you have 5000 rabbits)*.
But for Factorials as you expand what you know into new regions there are some very interesting consequences (which I don't understand, if I did I'd be a millionaire)

*

Spoiler

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There are multiple ways you could extend it the Fibonacci, that allow it to deal with unexpected questions.

E.g. with a step shape (representing a breeding season)
total population collapse (going to seed/bulbs over the winter)
smoothly and analytic
a combination of the above
overshooting then being brought down

In theory "Anything can happen", between the gaps. However somethings are more sensible than others and make much better choices. And that seems familiar...