The form i)ndiktiw/n is a transliteration of Latin indictio, and i)/ndiktos is a later Greek synonym for i)ndiktiw/n.
An indictio in early imperial Latin is an "imposition of taxes", but starting in 287 Diocletian introduced a new tax assessment system based a five-year period; the idea was probably based on the old five-year lustrum, a republican religious ceremony theoretically held every five years after the completion of a census. Beginning in 297 Diocletian's five-year system, originally called e)pigrafh/, received the additional name indictio. In 314 a fifteen-year indictio was first instituted by Licinius (rather than by Constantine the Great as often assumed), and was made to start retroactively from 312; each indictio began on September 23, the birthday of Augustus. Later, between 452 and 459, the beginning of the indictio was changed to September 1 to simplify calculations.
Starting as early as 356, in Cod. Theod. 12.12.2, indictio was being used as a method of dating based on the relative year within a fifteen-year period: that is, "quarta indictione" or "i)ndiktiw=ni d /" meant "in the fourth year [out of fifteen] of the indiction" (not "in the fourth indiction"). The individual fifteen-year indictiones were never numbered sequentially. See (on this and in general) E.J. Bickerman, Chronology of the Ancient World (1968) 78-79.
Constantine Porphyrogenitus (De Thematibus Europ. 8) cites from Hesychius an anecdotal etymology of i)ndiktiw/n. Supposedly Augustus named it from "i)naktiw/n" in reference to his victory at Actium (31 BCE), and the fifteen-year duration supposedly reflected the fact that Antony and Octavian had been co-consuls for fifteen years before Octavian, the future Augustus, conquered him and became sole ruler.
For further source citations for the usage of indictio and i)ndiktiw/n, see Lampe (1961-8), TLL (1934-64), or Sophocles (1887). For a discussion of the term and bibliography, see s.v. indictio in Cancik & Schneider (1996, Eng. trans. 2005), or consult web address 1 (Catholic Encyclopedia), web address 2 (German Wikipedia), and web address 3 (Dictionnaire des antiquités grecques et romaines).