Thread: Recursion help.

I have a general question about recursion. When you're either evaluating a recursive definition like:

for

and trying to find a general formula for

or trying to give a recursive definition for a formula like:



Is there an easier way to do it then look at the sequence and try to find some pattern between the 2 formulas, because I'm really bad at figuring about patters in sequences and forming formulas from them.

Any help would be greatly appreciated. Thank you.

In answering this, here is something I do not usually do: give a detailed answer.
But it may help you to see how we work on problems.
I used a computer algebra system to produce some 15 terms of the example.


From that brief table, we see blocks of three and powers of two.
It then took some time to find a closed form of the sequence.
Here is what I found using the ceiling function: