What does "order of growth decreases exponentially" mean? I understand than function decreases exponentially, then order of growth of this function is exponential with negative exponent. But what does it mean that order of growth decreases exponentially?

I don't understand what should i look for in this exercise:


  Exercise 2.33 Find a recurrence describing a sequence for which the order of growth decreases exponentially for odd-numbered terms, but increases exponentially for even-numbered terms.


Could you provide several first items of such a sequence to let me understand the exercise?
I think it just wants a recurrence for a sequence where the even-numbered terms increase exponentially and the odd-numbered terms decrease exponentially. Talking about the order of growth changing sounds like some kind of second-derivative property but I think it’s just poor phrasing.

To be absolutely sure, you’d have to ask the person who wrote the exercise.