## recurrence relation

An equation that defines each element of a sequence in terms of one or more earlier elements. E.g. The Fibonacci sequence,

X[1] = 1 X[2] = 1 X[n] = X[n-1] + X[n-2]

Some recurrence relations can be converted to "closed form" where X[n] is defined purely in terms of n, without reference to earlier elements.