Apparently Carmack didn't actually use it anyway, so I suppose there wasn't any purpose. But Carmack's series is significantly different from the normal Fibonacci series, because it only consists of the first ten elements, which isn't enough time to converge. If it was used in actual graphics or gameplay, it would have had a significantly different effect than a normal Fib sequence.

I just thought it was interesting, and another example of the same type of style which led to rocket jumping or bunnyhopping, which were also accidents.