Append the first 3 characters from the next sequence to the end of the current sequence. Keep a variable holding how many items you started with, and use that to control the loop, instead of using $i<@gene directly:

my @gene = split //, $seq[$i];
my $count = @gene;
if($i < $#seq) { 
    push @gene, split //, substr $seq[$i+1], 0, 3;
}
# Now, proceed as before:
for (my $i=0; $i<$count; $i+=3)    {
    ...
}
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p.s. You don't actually need to split the strings into arrays, a plain proper use of substr will work just as fine, as in:

   substr($genestring, $i, 1)
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