now this is a puzzle!, page-16

numbbat, you have to keep the same reasoning throughout the whole sequence. You can't have one scheme for line 1 and 2, and then have another scheme for line 3 and then a different scheme again for line 4 :p

My first solution exploits a vertical sequence. Which I don't think is the solution sought because Theabyss tells us to read from L to R then T to B.

My second solution is what I think LJAg is trying to explain.
Which is:

Line 1 reads a 1
Line 2 reads a 1 1
Line 3 reads 2 1
Line 4 reads 1 2 then 1 1
Line 5 reads 1 1 then 1 2 then 2 1, Thus line 6 should read 3 1 then 2 2 then 1 1, And thus line 7 should read 1 3 then 1 1 then 2 2 then 2 1.