code: import java.util.ArrayList;
  import java.util.List;
  
  public class Zeckendorf {
  
      private List<Integer> getFibList(final int maxNum, final int n1, final int n2, final List<Integer> fibs){
          if(n2 > maxNum) return fibs;
  
          fibs.add(n2);
  
          return getFibList(maxNum, n2, n1 + n2, fibs);
      }
  
      public String getZeckendorf(final int num) {
          if (num <= 0) return "0";
  
          final List<Integer> fibs = getFibList(num, 1, 2, new ArrayList<Integer>(){{ add(1); }});
  
          return getZeckString("", num, fibs.size() - 1, fibs);
      }
  
      private String getZeckString(final String zeck, final int num, final int index, final List<Integer> fibs){
          final int curFib = fibs.get(index);
          final boolean placeZeck = num >= curFib;
  
          final String outString = placeZeck ? zeck + "1" : zeck + "0";
          final int outNum = placeZeck ? num - curFib : num;
  
          if(index == 0) return outString;
  
          return  getZeckString(outString, outNum, index - 1, fibs);
      }
  
      public static void main(final String[] args) {
          final Zeckendorf zeckendorf = new Zeckendorf();
  
          for(int i =0; i <= 20; i++){
              System.out.println("Z("+ i +"):\t" + zeckendorf.getZeckendorf(i));
          }
      }
  }
  