Basically I created a dummy data in Excel by creating dates (from 1-1-2017 to 2-2-2021) and filling some random values (unif dist *5000) against these.
I added Week[date] to columns and year[date] to rows as in your screenshot. I added sum(value) on the text marks card.
Thereafter, I added table calculation --> Moving average --> edited it for previous 4 values , next 0 values, (check current value if you want to include current record), then check Null if there are not enough values. (your requirement). --> click compute using -Specific Dimensions change the order of fields below - drag Year above than week (table across then down will also create the same view)
You should be able to get a view as desired.
Regarding your query on number of days in the week, Tableau caters it automatically if you have chosen it datepart.
Edit I verified this in Excel, the method is correctly working.
See, the average of first 28 values in Excel
and the view built in tableau:
Here's the corrected dashboard hosted on Tableau Public.
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