The Christmas stocking theorem, also known as the hockey stick theorem, states that the sum of a diagonal string of numbers in Pascal's
triangle starting at the 
th entry from the top (where the apex has 
) on left edge and continuing down 
rows is equal to the number to the left and below (the "toe")
bottom of the diagonal (the "heel"; Butterworth 2002). This follows from
the identity
 |
where 
is a binomial coefficient.
