Depending on the mass of a star, the Oddo-Harkins pattern arises from the burning of progressively more massive elements within a collapsing dying  star by fusion processes such as the proton-proton chain, the CNO cycle, and the triple-alpha process.  The newly formed elements are ejected slowly via stellar wind, or in the explosion of a supernova, and will eventually join the rest of the galaxy's interstellar medium.