Insert a customized series as a new column in a DataFrame with Pandas

Question

Given this DataFrame with columns: category, Year, and Profit

data = {'category':pd.Series(['A','A','A','A','A','A']),
        'Year':pd.Series([1,1,3,3,3,4]),
        'Profit':pd.Series([10,11,5,6,30,31])}
df = pd.DataFrame(data)
display(df)

how can I insert numbers creating a new column Numbering by the following rule without manually enter the numbers one-by-one:

1. Insert 0 for the corresponding Year < 3.
2. Insert 1 at the first cell with Year >= 3.
3. After that insert a geometric series with a common ratio of 0.5 for the corresponding Year >= 3.

The desire output is displayed as follows:

Answer 1

We can try cumsum

s = (0.5**(df.Year.ge(3).cumsum()-1)).mask(df.Year<3,0)
Out[15]: 
0    0.000
1    0.000
2    1.000
3    0.500
4    0.250
5    0.125
Name: Year, dtype: float64
df['numbering'] = s