Count the ordered sequences of order sizes, each taken from a given set of distinct positive integers, that add up to exactly n shares.

You want to buy exactly n shares and may place any number of orders in sequence; each order fills an amount equal to one value from a given array of distinct positive integers k. Count the distinct sequences of orders that total n (order matters), returning 0 if impossible. Example: n = 3, k = [1, 2] gives 3 (1+1+1, 1+2, 2+1).