Elegance, of course, is in the eye of the beholder.

my $init  = 1;
my $step  = 4;
my $count = 5;                                                        
+                        
my $string = join ' ' => 
             map { $_ * $step - ($step - $init) } 
                 1 .. $count;
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If your code works, there's nothing wrong with it.