With an offline system, you cannot generate an incrementing serial number because you cannot talk to the other devices in your campaign to ensure uniqueness.
If you want a truly unique serial number, each form already generates a unique UUID that's available at meta/instanceID. It's a very long large number (e.g., uuid:9a1d5ce2-e09d-48d4-96f8-21c223eef304) to ensure uniqueness.
If you want to have some incremental counter that only works on one device, then try the ODK Counter app which does that. Incremental counter has more.
If you want some human-readable and probably unique ID, then you'll have to make your own from data in the form (e.g., district_id + head_of_household_name + enumerator_id + todays_date).