The Mordechai is the earliest source of the minhag which was not yet widely established in his days (d. 1298). The Rosh, his contemporary did not hold of it.
One reason given is that kitniyos could be ground into flour resembling the 5 grains. Therefore corn SHOULD be included. Peanuts are a legume, the original minhag was not to eat legumes, so it SHOULD also be included.