has the following combinatorial proof. One may show by induction that counts the number of ways that a strip of squares may be covered by and tiles. On the other hand, if such a tiling uses exactly of the tiles, then it uses of the tiles, and so uses tiles total. There are ways to order these tiles, and so summing this coefficient over all possible values of gives the identity.
has the following combinatorial proof. One may show by induction that counts the number of ways that a strip of squares may be covere.d by and tiles On the other hand, if such a tiling uses exactly of the tiles, then it uses of the tiles, and so uses tiles total. There are ways to order these tiles, and so summing this coefficient over all possible values of gives the identity.