We calculate the number of permutations with a given Ascent-Descent (A-D) sequence and find the generating function for the permutations with that sequence. Foulkes (1976) calculated the number by associating permutations with an up-down sequence. We discuss the relation between the A-D sequence and the up-down sequence and present two GAP programs with which we can compute the number of permutations with a given A-D sequence and an up-down sequence, respectively. We also explore which method of computation is more time-efficient when computing these numbers.