I'll have to do this as pseudocode since my original has a lot of other stuff intertwined. I think I extracted the gist of it OK though.
Inputs: Item1. Item2, Item3, Item4 (sensors from items)
Output: External Counter (Increment line to external counter)
Internals: Counter1, 'Do Pulse', Timer1, 'Timer1 is done', Timer2, 'Timer2 is done'
If Item1 (one shot) THEN increment Counter1
If Item2 (one shot) THEN increment Counter1
If Item3 (one shot) THEN increment Counter1
If Item4 (one shot) THEN increment Counter1
If Counter1 > 0 then turn on 'Do Pulse'
If 'Do Pulse' AND NOT 'Timer2 is done' THEN Timer1 (on time for output pulse)
If 'Do Pulse' AND NOT 'Timer1 is done' THEN turn on External Counter
If 'Do Pulse' AND 'Timer1 is done' THEN Timer2 (off time for output pulse)
If 'Do Pulse' AND 'Timer2 is done' THEN decrement Counter1