Formula to use instead of model

[BTH]

Scenario: An average of 5 test subjects are brought into a study in subsequent months and are administered 1 monthly test for as long as they remain part of the study. The time they remain in the study is 3 months.

Could someone please explain a formula or technique to sum the number of expected tests per month and total if possible in lieu of having to model it out like below to capture the dynamic of subjects rolling on and off over time? My real example has many more subjects and time on study varies, so a formula would save a lot of time at scale.

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[Greg]

I don't think there's anything that's going to make this more convenient than counting the number of users enrolled during a particular month. Using a spreadsheet will speed things up somewhat.