difference equation

differenssiyhtälö puhekieltä An equation involving an ordered sequence or real numbers (\left\{a_n\right\}_{n=1}^\infty) and some number if it's differences, where the first difference is defined as \Delta(a_n) = a_{n+1} - a_n\, and the kth difference is defined recursively as \Delta^k(a_n) = \Delta^{k-1}(a_{n+1}) - \Delta^{k-1}(a_n)\,.
puhekieltä more broadly, any recurrence relation