This is was happened to the first two Williams of Aquitaine, which is why we start with III:
William I "the Pious" Duke d'Aquitaine was married to Engelberge of Provence. He was son of Bernard, son of William of Gellone. He dsp. and was succeeded by his nephew, William II "the Younger" Duke of Aquitaine 918-26. Neither of these two first William Dukes of Aquitaine had any children.