Suppose the components of x = hx 1 , x2, . . . , xni are all different, except for a single pair of identical elements that are separated by k other elements. For example, PYTHAGOREAN has n = 11 and k...

Suppose the components of x = hx₁,
_x2,
. . . , xni are all different, except for a single pair of identical elements that are separated by k other elements. For example, PYTHAGOREAN has n = 11 and k = 4, because there are four entries (GORE) between the As (at index 5 and 10), which are the only repeated entries. In terms of n and k, how many subsequences of x are there?