How to solve 2 variable recursion?

T(m,n) = T(m-1,n) + T(floor(m/2), n-1)

Base conditions
T(m,n) = 1 when n = 0
T(m,n) = 0 when m < n

Edited: Below is the code for which I want to know the time complexity in terms of m and n.

#Python3 program to count total number of
#special sequences of length n where
#Recursive function to find the number of
# special sequences
def getTotalNumberOfSequences(m,n):

#A special sequence cannot exist if length
#n is more than the maximum value m.
if m<n:
return 0

#If n is 0, found an empty special sequence
if n==0:
return 1

#There can be two possibilities : (1) Reduce
#last element value (2) Consider last element
#as m and reduce number of terms
res=(getTotalNumberOfSequences(m-1,n)+
getTotalNumberOfSequences(m//2,n-1))
return res

#Driver Code
if __name__=='__main__':
m=10
n=4
print('Total number


of possible sequences:',getTotalNumberOfSequences(m,n))

• Please edit the question to add a reference to the original problem. – Apass.Jack Jun 18 at 18:50
• As a first step to solve the recurrence equation, please edit the question to list the first values of $T(m,n)$. For example, all $T(m,n)$ for $m, n\le 6$. – Apass.Jack Jun 18 at 18:52
• How do you interpret $m/2$ when $m$ is odd? – Yuval Filmus Jun 18 at 21:09
• @YuvalFilmus we take floor of m/2 when m is odd. – Prarthit Mehra Jun 19 at 4:36
• It looks like it is not easy to find a tight bound for its time-complexity. – Apass.Jack Jun 19 at 17:34