Until this discussion, I never knew that Asara bTevet could be on Friday two days in a row. I think the only way is if in the first year, Rosh Hashana is on Shabbos in a leap year with 383 days, and the second year Rosh Hashana is on Thursday in a regular year of 355 days.
myappel:- Not 2 days in a row, but 2 years in a row. But yes myapel, the 2 types of years which you described was absolutely on the ball & correct.
Any time that Assoro b’Teves is 2 years running on a Friday, the Assoro b’Teves immediately preceding them as well as the one immediately following them are both on a Tuesday.