I don't like that there are still wrong moves possible*, probably because I din't follow my own concept...

use strict;
use warnings;
use Data::Dump qw/pp dd/;


my $goal = [3,1];
my ($nl,$nr) = @$goal;

my @results;

pathfinder( [0,0] );                      # start

pp \@$_ for @results;


sub pathfinder {
    my ( $last )=@_;

    my ($l,$r)   = @$last ;

    if ( $nl == $l ) {
        if ($nr == $r){
            push @results,[ reverse @_];
        }
        else {
            #warn "wrong",pp \@_;
            return
        }

    }


    # left
    pathfinder( [$l+1,$r  ], @_ ) if $l != $nl;

    # right
    pathfinder( [$l+1,$r+1], @_ ) if $nr != $r;
}
[download]

[[0, 0], [1, 0], [2, 0], [3, 1]]
[[0, 0], [1, 0], [2, 1], [3, 1]]
[[0, 0], [1, 1], [2, 1], [3, 1]]
[download]

*) i.e. the else branch with the warning should never be reached.

update

solution here