I wonder just how mandatory it is to use the plural form of seachtain after numbers (from 3 up). I was taught that ceann and bliain had to be pluralised but that a range of other words could be, but not necessarily so: pingin, seachtain, troigh, orlach, cloigeann and more.
Leaving aside the fact (?) that using the plural form of all nouns is acceptable too (didn't I see that mentioned before?), the reason for accepting sé throigh/sé troithe was because of dialectal variations.
I state the above more as a question than anything else, and I ask in reference to the Caighdeán.
I would certainly say trí seachtaine (and I'm aware of trí seachtainí) but can trí sheachtain be ruled out completely?
According to what I saw in the 3 "An Teanga Bheo" and in Tobar na Gaedhilge, the rule is right in Connemara, Corca Dhuibhne and Ulster.