You could try this:

$ cat 652805.pl
#!/usr/bin/perl -w
#
# Generate all possible subsequences of sequence 1
#
use strict;
use warnings;

# Sequence 1
my @seq_1 = ('a', 'b', 'c', 'd', 'e');

# Count of all possible subsequences
my $s1_max = 2 ** @seq_1;
print "Number of possible subsequences: ", $s1_max,"\n";

# To get each possible subsequence, use a binary number
# as a mask to tell you which digits to print
for my $seq (0 .. $s1_max-1) {
        print "Sequence ", $seq, ": ";
        my $bit = 0;
        while ($bit < @seq_1) {
                print $seq_1[$bit], " " if 2**$bit & $seq;
                ++$bit;
        }
        print "\n";
}
[download]

Not the most efficient solution, but I tried to make it easy to read for you...

...roboticus