Code to count card combinations according to this math.SE question: http://math.stackexchange.com/questions/129580

Question129580.java

import java.util.ArrayList;
import java.util.List;

public class Question129580 {
    static List<int []> getPermutations (int n) {
        return getPermutations (n,n);
    }

    static List<int []> getPermutations (int n,int k) {
        List<int []> permutations = new ArrayList<int[]> ();
        makePermutations (permutations,new int [k],new boolean [n],0);
        return permutations;
    }

    static void makePermutations (List<int []> permutations,int [] permutation,boolean [] used,int j) {
        if (j == permutation.length)
            permutations.add (permutation.clone ());
        else
            for (int i = 0;i < used.length;i++)
                if (!used [i]) {
                    permutation [j] = i;
                    used [i] = true;
                    makePermutations (permutations,permutation,used,j + 1);
                    used [i] = false;
                }
    }

    public static void main (String [] args) {
        for (int n = 1;n <= 4;n++) {
            int k = (n * (n + 1)) / 2;
            int count = 0;
            outer:
            for (int [] p : Permutations.getPermutations (k)) {
                for (int i = 0;i < n;i++) {
                    for (int j = (i * (i + 1)) / 2,l = 0;l < i;l++,j++) {
                        if (Math.abs (p [j] - p [j + 1]) == 1)
                            continue outer;
                    }
                }
                count++;
            }
            System.out.println (n + " : " + count);
        }
    }
}