What is the pattern for Instagram photo URLs?

When uploading a photo to Instagram, a unique URL is generated (e.g. http://ift.tt/19OAyGF or http://ift.tt/1E0VLJP). I've noticed that

1. the strings at the end of the URL are more or less sequential (though they seem to loop back every few months),


2. not every string has a photo associated to it (e.g. http://ift.tt/1CjSuQe and http://ift.tt/1E0VLJV link to nothing)


3. and the strings consist of upper- and lower-case letters, numbers and the underscore character.

If I knew the timestamp of a photo and its uploader, would it be possible for me to know the URL string as well? Ideally, my goal would be to know that if I uploaded a photo at a certain time, I could know in advance what its URL would be.

More generally, if I had a large database of strings, how would I go about in trying to reverse engineer the way the strings are generated?