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perl -le'$==1,(1x$_)=~/^(1|11)*(?{$=++})^/,print$=for 0..20'

perl -le'$==1,(1x$_)=~/^(1|11(??{}))*(?{$=++})^/,print$=for 0..20'

perl -le'$==0,(1x$_)=~/^(1|11(??{}))*$(?{$=++})^/,print$=for 0..20'

 1  (1)(1)(1)(1)(1)(1)
 2  (1)(1)(1)(1)(1  1)
...
11  (1  1)(1)(1  1)(1)
12  (1  1)(1  1)(1)(1)
13  (1  1)(1  1)(1  1)

 1  (1)(1)(1)(1)
 2  (1)(1)(1) 1
...
10  (1  1)(1  1)
11  (1  1) 1  1
12   1  1  1  1