dirt (verbose mode), 17 bytes

"1 2 1"|1" 2 2".* 

Run as dirt ones_and_twos.dirt -v -i ""

Outputs each element of the sequence on a new line.

dirt (verbose mode), 17 bytes

"1 2 1"|1" 2 2".* 

Run as dirt ones_and_twos.dirt -v -i ""

Outputs each element of the sequence on a new line.

Alternatively, if we allow new lines between some but not all elements,

dirt (verbose mode), questionable format, 13 bytes

"121"|1"22".* 

prints

121 12221 1222221 122222221 12222222221 1222222222221 122222222222221 12222222222222221 ...