CLASSIFICATION OF GENERALIZED PAPER FOLDING SEQUENCES

Generalized paper folding sequences X n and (XpYq) n where X;Y 2 fR;L;U;Dg, and n;p;q2 N with p;q 2 are clas- sied in this paper. We show that all generalized paper folding sequences X n p are classied into one type if we classify generalized paper folding sequences along with the numbers of downwards and upwards. In addition, we investigate the numbers of downwards and upwards in (XpYq) n and prove that all generalized paper fold- ing sequences (XpYq) n are classied into two types.