As per the statement ‘Upanayanam bhramanasya ashtamE’, Upanayanam is performed in the eight year. Some perform this on the 8th year after conception.
But there are no restrictions on conducting Upanayanam during odd-numbered ages. It is ordained that it must be performed before 16 years old; if conducted after 16 years, Gayathri mantra will not yield any benefit. Upanayanam can be performed any time between 7 and 16 years of age. There are no authoritative statements (Pramaanam) that mandate the performance of Upanayam either during odd or even-numbered ages.