The two above relations allow transforming a recurrence relation of order into a difference equation of order , and, conversely, a difference equation of order into recurrence relation of order . Each transformation is the inverse of the other, and the sequences that are solution of the difference equation are exactly those that satisfies the recurrence relation.
The two above relations allow transforming a recurrence relation of order into a difference equation of order  and, conversely, a difference equation of order into recurrence relation of order . Each transformation is the inverse of t,he other, and the sequences that are solution of the difference equation are exactly those that satisfies the recurrence relation.