For completeness, the following works too:

use strict;
use warnings;

use Data::Dumper; 

use constant HASHREFCONST => do {
   my $hashref  =
     {
      'ONE'   => 1,
      'TWO'   => 2,
      'THREE' => 3,
      'FOUR'  => 4,
     };
   [$hashref->{ONE} .. $hashref->{FOUR}]
};


print Dumper(HASHREFCONST);
[download]

$VAR1 = [
          1,
          2,
          3,
          4
        ];
[download]

Depends what your real intention is...

Update

for instance the use of a range .. looks very dubious!