Counting values based on varying dates in R

Question

I am having a problem that requires me to count the number of observations in the response column (1s and 0s only) grouped by IDs and based on varying reference dates. I am thinking of using dplyr summarise as a solution but I could not make it work if I take into consideration the said dates.

Sample Data:

CustomerID   AccountID     OpenDate     Response
   AAA         456        2020-01-01        1
   AAA         456        2020-01-03        1
   AAA         456        2020-01-05        1
   BBB         789        2020-02-01        1
   BBB         789        2020-02-22        0
   BBB         789        2020-03-01        1

Desired Count Result:

CustomerID   AccountID     OpenDate       Count
   AAA         456        2020-01-01        1
   AAA         456        2020-01-03        2
   AAA         456        2020-01-05        3
   BBB         789        2020-02-01        1
   BBB         789        2020-02-22        1
   BBB         789        2020-03-01        2

Notice that as the dates go farther, the response count increases because it took into consideration the movement of days.