What fields in the record are blank? If A, B, and C are fields in the record, then there would be nothing to concatenate. If they are not fields in the record, you don’t need a formula.
If you you have specific input fields that would be blank, and other fields that would not be blank, you can create an if statement with those.
IF( AND({Input 1} = BLANK(), {Input 2} = BLANK(), {Input 3} = BLANK())
A & B,
B & C
)