Auto generate new form fields in form builder?

So, I need to do something like this:  A user enters the page, and sees a drop down list of numbers.  If the select 1, then a row of text fields appear below, ready for input.  If they select 3, then 3 rows appear, ready for input.  I obviously can code this with javascript, but i need the forms to be recognizable by the form builder and I need to be able to submit that data, whether 1 row or 20 rows into a database (using an integration component).  Anyone have an idea how to make these dynamically created (and dynamically named) rows?