The Collaborative International Dictionary of English v.0.48:

Triweekly \Tri"week`ly\, a. [Pref. tri- + weekly.]
   Occurring or appearing three times a week; thriceweekly; as,
   a triweekly newspaper. -- adv. Three times a week. -- n. A
   triweekly publication.
   [1913 Webster]

   Note: This is a convenient word, but is not legitimately
         formed. It should mean occurring once in three weeks,
         as triennial means once in three years. Cf. Biweekly.
         [1913 Webster]