Generate random time series data with increasing trend

Is there a way in Python to spread a population over a period of time with an increasing trend?

For instance, assuming I have 1000 people to distribute between 1901 and 2000, the result I expect is like:

result = {1901: 6, 1902: 4, 1903: 8, 1904: 8, ..., 1997: 20, 1998: 22, 1999: 18, 2000: 21}

The sum of the values ​​in the dictionary result (6 + 4 + 8 + 8 + ... + 20 + 22 + 18 + 21) should be 1000. It should be possible to adjust the value of the first year and that of the last (to determine how much the series should be increasing)