Can someone explain the pattern in the picture?

At first you have 1 and then 1 and 1 and you know that 1+1=2 so you have 1, 2, 1, and then you know that 1+2=3 and  2+1=3 so yu have 1,3,3,1 and then you know that 1+3=4 and 3+1=4 so you have 1,4,4,1 and it goes like that until the end.