What's next in the sequence?

Originally posted by Fat Lady
Antrim
Armagh

Carlow
Cavan
Clare
Cork

Donegal
Down
Dublin

Fermanagh

Galway

Kerry
Kildare
Kilkenny

Laois
Leitrim
Limerick
Londonderry
Longford
Louth

Mayo
Meath
Monaghan

Offaly

Roscommon

Sligo

Tipperary
Tyrone

Waterford
Westmeath
Wexford
Wicklow


Obviously this puzzle would have been trivial if you hadn't got the 13th digit wrong.

Ah, missed that, thought I got them all right, but still no solutions came forward till I started giving big hints. I made up this puzzle from one I saw in the 'Ask Marylin" column in our sunday paper, but it was based on states in the US. So I changed it to counties in Ireland. I made it a bit trickier by not including the last two letters, Y & Z in the list to throw people off if they totaled everything, which would be screaming out 26! But if someone got so far as to notice I did 2 M's instead of 3, they would have still solved it.