Probably the easiest way to do it is to use Time::Local's timelocal_nocheck function to convert the day number back to seconds, and then use localtime to extract what you want.

#!/usr/bin/perl

use strict;
use warnings;

use Time::Local qw(timelocal_nocheck);

my $yday = 244; # September 1st, 2004

my @a = localtime(timelocal_nocheck(0,0,0,$yday+1,0,4)); # 2004

# remember: watch out for 0.  mon == 8 is Sep, not Aug
print "$a[6] $a[4] $a[3]\n"; # wday, mon, mday
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