yes both the recurrences are same here.
Just to give you an idea about where may be the difference of recurrence relation.Consider two functions A() & B().
A(n) {
if(n<=1) return 1;
else
return ( A(n/2) + A(n/2) + n );
}
Recurrence for Time Complexity : T(n) = 2*T(n/2) + 1
Recurrence for Value : T(n) = 2*T(n/2) + n
B(n) {
if(n<=1) return 1;
else
return ( 2*A(n/2) + n );
}
Recurrence for Time Complexity : T(n) = T(n/2) + 1
Recurrence for Value : T(n) = 2*T(n/2) + n
In this A and B both will return the same value so for getting value for some number n,they will result in same but both the functions having different time complexity as you can see we are getting separate recurrence relation for time complexity.
For Function A, we are getting 2*T(n/2) because we are going to call same function 2 time but in function B,we are taking only T(n/2) because we are calling function only one time after getting the value of T(n/2) we are simply multiplying it by 2.
