How to get Facebook notifications on iPhone 4?

I have an iPhone 4 along with the Facebook app but the it doesn't show up in the notification centre. It's the same on my iPod and I can't figure out why. I have tried deleting the app and downloading it again but nothing works. I have also looked inside the app itself and all of the boxes are ticked under notifications. Does anyone know how I can get push notifications from my Facebook app?
Thank you.

Added (1). It doesn't show up in my notification center. (in settings)

Settings>notifications>facebook