hockey stick theorem

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 nth entry from the top (where the apex has n = 0) on left edge and continuing down k 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 sum_(i = 0)^(k - 1)(n + i i) = (k + n k - 1), where (n k) is a binomial coefficient.

binomial coefficient | binomial sums | Pascal's triangle | star of David theorem