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**how to find a mathematical formula for this recursion??**

i got this recursion

Code:

```
int b(int n,int count) {
int i;
count =a(n,count);
for(i=0;i<n;i++)
count =b(i,count);
return count;
```

b(0,0)=1

b(1,0)=3

b(1,1)=4

b(2,0)=8

the formula for function "a" is a(n,c)=2^n + c

what is the formal way to find a formula for b

so i could predict whats the output of each input like b(12,15)??

i dont have any intuition

i am looking for the formal way