This is a simple challenge problem I made up myself. Consider the sequence
The first term is 1, and successive terms are formed by multiplying the previous term by 2 and 3 alternately, starting with 2. Thus
and so on.
If is odd, then disappears, leaving the other half. If is even, the other half disappears, leaving this one. Neat, yeah?
This method is very handy for writing down a formula for sequences whose properties alternate between odd and even terms. For example, suppose you have