Computed column 'IsWeekend' in table  cannot be persisted because the column is non-deterministic
You can do a datediff between 1900-01-01, that just happens to be a monday, and check if modulo 7 is a 5 or a 6.

create table D
(
  DateRecorded date,
  IsWeekend as cast(case when datediff(day, 0, DateRecorded) % 7 in (5, 6) 
                      then 1 
                      else 0 
                    end as bit) persisted
)


BTW, you don't need to persist the computed column in order to use it in an index.