GENERALIZED HOCKEY STICK IDENTITIES AND iV-DIMENSIONAL BLOCKWALKING

Traditionally, the word "abracadabra" was encrypted onto amulets and other magical paraphernalia to help ward off evil. George Polya ([8], [9]) provided the cryptic form of this word shown in Figure 1 and asked how many ways abracadabra can be spelled out using this diagram. If we replace the diagram in Figure 1 with the grid shown in Figure 2 where letters in the original diagram are placed at points of intersection of the grid, then the question is equivalent to asking how many paths there are from the top of the grid to the spade at the bottom of the grid where each step is either down and left or down and right. One such path that spells out abracadabra is shown. By considering this grid as a city street map, we can think of such paths as walking city blocks—or blockwalking.