Can't send texts to one particular friend, texts work one-way, phone calls work both way

For about a bit more than a month now, one particular friend (and just one, as far as I can tell) has not been receiving my text messages. He can send me texts messages and we are able to call each other. The texts emitted from my phone however, don't seem to go through. I have no indication that the text has not been delivered (no red exclamation point next to it). This particular person is not using an iPhone for this particular phone number.

I am using an iPhone 4 (32GB) running iOS 7.1.2.

I have tried many different things.

(1) I have checked that this friend was not in my block list. The block list is empty. But even if that person were in my block list, would I be able to receive texts and call? I have tried adding that person to the block list then sending a text. Then removing that person from the block list and texting again.

(2) Yesterday I have restored my phone from a backup. I then erased completely the (long) text exchange between me and this friend, waited for the phone to process the deletion and tried again to send a text. I then deleted the entire contact information of this friend. And then I texted the phone number.

None of these steps have worked. I'm very puzzled.

Has anyone ever been confronted to an issue like this one?