how to write optimal nested recursion functions

I'm trying to translate a complicated excel spreadsheet to python, here's a simple example of what the excel spreadsheet looks like:

r       a               b          c            d
1       2%             a(r)+1   b(r)*2+a(r)   100
2to100  d(r-1)*.0001   a(r)+1   b(r)*2+a(r)   d(r-1)*c(r)

Here's what I wrote:

def a(r):
  if r==1:
    return 0.02
  else:
    return d(r-1)*0.0001
def b(r):
  return a(r)+1
def c(r):
  return b(r)*2+a(r)
def d(r):
  if r==1:
    return 100
  else:
    return d(r-1)*c(r)

I understand this is a naive example and I don't need a, b and c and can combine everything into one recursive function, but the real spreadsheet is more complicated and it takes a lot of effort to combine them.

Now my question is with efficiency. if I write the recursive functions separately, function (a) is being called 3 times each step and will quickly get out of hand. Is there a way to write the function so (a) is only called once each step?

calling d(100) is equivalent of calling function (a) 3^100=5.1*10^47 times and is impossible to finish.

Thanks to Tuqay in the comment, adding the following code solved the problem and speed up d(100) to less than a second

from functools import lru_cache
@lru_cache(maxsize = 128)
def a(r):
  if r==1:
    return 0.02
  else:
    return d(r-1)*0.0001
def b(r):
  return a(r)+1
def c(r):
  return b(r)*2+a(r)
def d(r):
  if r==1:
    return 100
  else:
    return d(r-1)*c(r)/3