time machine backup file nam

I have deleted my time machine backups by accidentally formatting an external harddrive, as my device for the backup was stolen and the backup wouldn't fit on my new machine. the machine was recovered and now I don't have my backups, as i deleted them. I have done a hard drive scan on the external drive and it recovered a ton of formatted info but I don't know what file I'm even looking for. Does anyone know what file or group of file I would need to search to see if one of my old backups has been found?