Formulas of Counting to Move the Cups onto the Plates

Abstract

The purposes of this research were: to generate the formulas of counting on moving the cups onto plates (in case there are more plates than cups) by using recursion and induction proof.  The results found that moved the n cups onto the  m plates, we can generate the recursive formula and general formula were generated by

  and  

in order, and were able to prove the general formula by using the induction proof.