Iterating over all combinations is as simple as counting. Think of all values in the array to be calculated as being 0s or 1s. If it is a 1, the value is included and if it is 0, it isn't. For instance:

5  -6  8  10  12  3  10
0  0   0  0   0   0  1 = 10
0  0   0  0   0   1  0 = 3
0  0   0  0   0   1  1 = 3, 10
0  0   0  0   1   0  0 = 12
0  0   0  0   1   0  1 = 12, 10
...
1  1   1  1   1   1  1 = 5, -6, 8, 10, 12, 3, 10
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#!/usr/bin/perl
use strict;
use warnings;
use List::Util 'sum';

my @amount = (5, -6, 8, 10, 12, 3, 10);
my $count = @amount;

for (1 .. 2 ** $count - 1) {
    my @bit = split //, sprintf("%.${count}b", $_);
    my $total = sum( map {$bit[$_] ? $amount[$_] : 0 } 0 .. $#bit);
    print "$total\n";
}
[download]

I really can't see an elegant way to do a scan of all possible n-ple of an array without using a recursive sub

Elegance for the sake of elegance is what caused the famous quote about LISP programmers who know the value of everything and the cost of nothing.

TIMTOWDI, and different algorithms will do. My point being that our OP made a very odd choice for his foray into the world of recursions. There are ways of solving this recursively without blowing up the stack, but for a beginner, this doesn't look like the best thing to start with.