User blog comment:VoidSansXD/Possibly non-recursive function/@comment-37246647-20190218235317/@comment-30754445-20190219003127

Any function which can be calculated with a rigid finite step-by-step process is recursive.

For your cat-and-doors scenario, you can calculate C(n) by simply going through the scenario until you close the first door. So it's recursive.

An example of a non-recursive function:

f(n) = the maximum possible output of a standard C computer program with n characters (assuming infinite memory, infinite time and no integer overflow)