The recursive definition is intuitive and easy to come up with given its mathematical definition. To avoid redundant computation, the function can be memoized.

The recursive definition is intuitive and easy to come up with given its mathematical definition. To avoid redundant computation, the function can be memoized. Yes, you can write it linearly as well, but oftentimes the linear algorithm is harder to come up with. SICP spends a lot of time on this subject in one of its early chapters and its worth a read. Also, some languages support recursion better than others. Scheme is top notch in this regard as the standards do not specify a stack, meaning that implementations can do things like heap allocate stack frames that grow and shrink according to demand.