Patterns with (1,1,0) and (0,1,1) in denominators

Recall that when b₂=1,

as mentioned in 0114.

When (b₁,b₂,b₃)=(1,1,0),

When (b₁,b₂,b₃)=(0,1,1) instead,

Their consecutive forms

Patterns with 1,1,0,0,1,1,0,0,1,1,0,0,… in denominators

regarding the sequence of denominators as 1,1,0, and 0,1,1, and 0,0,1, and 1,0,0. The latter two were mentioned yesterday.