calc_number_possible.py

from functools import lru_cache

@lru_cache # Stores previously computed factorials
def factorial(num):
  if num < 2:
      return 1
  return num * factorial(num - 1)

def N(C, m_2, m_1, m_0):
  count = 0
  for i in range(C):
      if (C - i) % 2 == 0:
        continue
      count += (
          factorial(C-1)
          * m_2 ** ((C-i-1)//2)
          * m_1 ** i
          * (m_0 + 1) ** ((C-i+1)//2)
          // factorial((C-i+1)//2)
          // factorial((C-i-1)//2)
      )
  return count