The eX-Twitter pages concerning this format explicitly state that it's not meant for general use outside Twitter.

This reads like a one way hashing with DB lookup.

Hence I doubt there is a better algorithmic solution than querying Twitter for the (final?) redirect, like shown by other brethren.

update

The link service at http://t.co is only used on links posted on Twitter and is not available as a general shortening service on other apps or sites.