code: def ncoef_fmap(order):
      
  
      ncoef = 0
      for i in range(order + 1):
          for j in range(i + 1):
              ncoef += 1
      return ncoef
docs: Expected number of coefficients in a 2D transformation of a given order.
  
      Parameters
      ----------
      order : int
          Order of the 2D polynomial transformation.
  
      Returns
      -------
      ncoef : int
          Expected number of coefficients.