Thare are some other neat solutions to this problem at How to generate restricted partitions of an integer.

Of course, if you'll indulge me to demonstrate a silly way to do it, I'd use regexes on unary strings as I did in my other change-making posts {1, 2}:

my $amount = shift;
my $regex  = join "", map { "(1{$_})*" } @ARGV;
my $incr_x = qr/(?{$x++})/;
local $x;
(1 x $amount) =~ /^$regex(?:$)$incr_x(?!)/;
print "$x\n";
[download]