Variation in prefix sum

[Soham Mukherjee]

I'm attempting to parallelize some program that solves recursive 
linear equations. Some of these, I believe, might be modified 
into prefix sums. Here are a handful of examples of the equations 
I'm dealing with.
The conventional prefix sum is as follows:
```
y[i] = y[i-1] + x[i]
```
One equation that interests me is similar to prefix sum but with 
a multiplication:
```
y[i] = A*y[i-1] + x[i]
```
Another feature is deeper recursion:
```
y[i] = y[i-1] + y[i-2] + x[i]
```
Aside from these two versions, I'm wondering whether there are 
any resources that discuss how to convert situations like the one 
above into prefix sum form. Alternatively, ways for 
adopting/adapting prefix sum in order to make it more flexible. I 
read this [blog](https://www.scaler.com/topics/prefix-sum/), but 
I need more information about my situation.