CombinationCounter.java

import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.List;

public class CombinationCounter {

    private static List<BigInteger> generateCombinationLimitedBy(int index) {
        List<BigInteger> sequence = new ArrayList<>();
        sequence.add(BigInteger.ONE);

        final BigInteger two = new BigInteger("2");
        final BigInteger three = new BigInteger("3");
        for (int i = 1; i < index; i++) {
            for (int j = 0; j <= i; j++) {
                sequence.add(two.pow(j).multiply(three.pow(i - j)));
            }
        }

        Collections.sort(sequence, new Comparator<BigInteger>() {
            @Override
            public int compare(BigInteger big1, BigInteger big2) {
                return big1.compareTo(big2);
            }
        });

        return sequence;
    }

    public static void main(String[] args) {
        int index = Integer.parseInt(args[0]);
        List<BigInteger> sequence = generateCombinationLimitedBy(index);
        System.out.println("The " + index + "th number : " + sequence.get(index));
    }

}