As per Kant, all pure mathematics are synthetic a priori.
On the contrary, analytic judgement are those where the predicate is contained in the subject.
If we consider the concept of recursive function, say Fibonacci series 0,1,2,3,5,8,13,21 expressed by: F n= F (n-1) + F (n-2) what we get is the earlier or next number by adding/subtracting the previous one.
Take otherwise Fibonacci series or recursive function, the result is contained in the subject.
In that case do we consider Fibonacci series analytic/synthetic?