Question 498943
There are several books, no doubt some of them online.
It's easy enough to explain:
Once you see the pattern, say it's
1 3 7 15 31 ...
which you see is "double previous then add 1",
The recusive formula is not far off:
x(1)=1
for n>1, x(n)=2*x(n-1)+1
Even sequences that are "too easy" such as the even numbers,
can be expressed recursively:
x(1)=2
n>1: x(n)=x(n-1)+2