Lambs no more than one year old, And rams no more than two years old. When the Torah mandates bringing a lamb-offering, it must be within its first year. This is explicit in the Torah, see for instance Numbers 7:17. Rams adult sheep must be at least within their second year.
And all these years are reckoned from day to day. When counting the age of any of the animals listed in the first three mishnayot of this tractate, we count from the day the animal was born. We don't count from the beginning of the year, as we do for other matters. So a lamb born in the beginning of Elul is not considered to be one year old until the following Elul.
One that is thirteen months old is not valid, neither as a ram nor as a lamb. Rabbi Tarfon called it palges. Ben Azzai called it noked. Rabbi Ishmael called it parakhrigma. A 13 month old sheep cannot be considered a lamb or a ram. It is too old to be a lamb and a sheep is not a ram until it is 30 days past its first birthday. The 30 days is likely to be a vestige of the notion that the life of anything born is considered precarious until it has reached thirty days old. It's almost as if we count the animal's days only from one month and on (although this is only in cases in which the rule is stringent when it comes to the limit of a lamb, it is one year, and not 13 months). The sages all have a special name for this 13 month old sheep. Palges is a Greek word which refers to something that is no longer a child but has not reached maturity (kind of like a teenager). Noked is a type of inferior sheep. And parakhrigma is a Greek word used to refer to a coin with a king's image that has been invalidated by the new king. The 13 month old has been disqualified from being a "lamb" but has not yet been validated as a "ram."
If a man offered it he must bring for it the libation of a ram, but it is not counted as his offering. If a person sacrifices a 13 month old sheep he must bring the libations that are brought for a ram. This means 2 tenths of an ephah of flour, a third of a hin of oil and a third of a hin of wine (see Numbers 15:6-7). However, offering this animal doesn't count as fulfilling his obligation. So if he vowed to bring a ram or a lamb, the thirteen month old doesn't count and he still has to bring another one.
One that is thirteen months old behold it is a ram. Once it reaches 13 months and one day it is a ram.