[math-fun] First differences

Hello math-fun, Could someone explain me this sequence, designed by a friend of mine? He says it has to do with first differences... S = one, nine, nine, five, five, nine, nine, five, five, nine, one, three, thirteen, seventeen, one, three, thirteen, seventeen, nine, five, five, nine, nine, five, five, nine, one, three, thirteen, seventeen, one, three, thirteen, seventeen,... Best, E.