It does what you're trying to do, only with single values rather than arrays. I think I know what you're trying to do now, though I have no idea why:

use strict;
use warnings;

my @vals = ( [1,1,1],[0,0,0],[1,0,1],[0,0,1] );
my $n = 2;
my @solutions;

nSum(\@vals, \@solutions, [], -1, $n);

print "@$_\n" for @solutions;

sub nSum {
    my ($vals, $solutions, $sums, $i, $n) = @_;
    my (@sums, $j, $k);

    $n--;
    for $j (($i+1)..$#$vals) {
        @sums = @$sums;
        for $k (0..$#{$vals->[0]}) {
            $sums[$k] += $vals->[$j][$k];
        }
        if ($n) {
            nSum($vals, $solutions, \@sums, $j, $n);
        }
        else {
            push @$solutions, [@sums];
        }
    }
}
[download]

You can change the number of elements in the arrays or AoA's and also the value for $n and you should get accurate results regardless.