I like the look of \$$\lceil \frac{n}{2} \rceil\$$ a lot more than \$$\lfloor \frac{n+1}{2} \\rfloor \$$, because it goes along better with my story about the "best approximation from above" to \$$\frac{n}{2}\$$. That's why I was so confused by Alex Varga's answer. But they're equal! You learn something new every day.

I don't know a name for this phenomenon, Cole.