In the 12 days of christmas, since there are 12 verses and the first n lines repeat every verse, it's actually n*(13 - n) in total, so 12 partridges, 22 turtle doves, etc.
Here are the actual totals
On an unrelated note, anyone need 41 swans a-swimming?
if you want to know how many gifts you'll receive on the nth day of Christmas, it's
(n^2 + n)/2, or
n+1 choose 2, the triangular numbers
1 3 6 10 15 21 28 36 45 55 66 78
if you want to know how many gifts you have total on the nth day of Christmas, it's
(n^3 + 3n^2 + 2n) / 6
or n+2 choose 3, the tetrahedral numbers
1 4 10 20 35 56 84 120 165 220 286 364
Worm