If the elements of the cell array are row vectors, you can do this:
union_ids = unique( [encounter_ids{:}] );
if they are column vectors, use:
union_ids = unique( vertcat(encounter_ids{:}) );
If you're not sure if they are both (some are row vectors, some are columns), you can make them be all column vectors:
encounter_ids = cellfun(@(c)c(:), encounter_ids, 'UniformOutput',false);
union_ids = unique( vertcat(encounter_ids{:}) );
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