Recurrence relation problem
Hi I'm studying for my finals and having trouble with this question:
Consider the following recurrence relation:
for where .
Write the corresponding generating function in its closed form.
I've set up the generating function as
and I've gotten as far in my working as:
But according to the solutions I should at this stage be getting:
What am I doing wrong?
I'd really appreciate some help on this one, thanks in advance!
Re: Recurrence relation problem
We have the following table where I called the function in the last row F(z):
In the right part of the table (after the vertical line), the first row equals the sum of the other rows. Using , this gives