#!/usr/bin/perl

use strict; # https://perlmonks.org/?node_id=11114280
use warnings;
use List::Util qw( uniq );

my @cache = [];

for my $n ( 3 .. 4 )
  {
  print "$_\n" for sort @{ find($n) };
  print "\n";
  }

sub find
  {
  my $n = shift;
  $cache[$n] //= [ uniq $n, map { my $nn = $_;
      map { my $t = $_; map "$t+$_", @{ find($nn) } } @{ find($n - $nn) }
      } 1 .. $n - 1 ];
  }