Find poetic derangements; see https://math.stackexchange.com/questions/3617128.

Question3617128.java

public class Question3617128 {
    static long count;
    
    public static void main(String [] args) {
        for (int i = 1,n = 1;;i++,n += i) {
            count = 0;
            recurse (new boolean [n],new int [n],new int [i + 1],0);
            System.out.println(n + " : " + count);
        }
    }
    
    static void recurse (boolean [] used,int [] p,int [] counts,int i) {
        if (i == used.length) {
            count++;
            for (int x : p)
                System.out.print((char) (x + 'A'));
            System.out.println();
        }
        else
            for (int d = 1;d < counts.length;d++)
                if (counts [d] < d)
                    for (int sign = -1;sign <= 1;sign += 2) {
                        int j = i + d * sign;
                        if (0 <= j && j < used.length && !used [j]) {
                            used [j] = true;
                            counts [d]++;
                            p [i] = j;
                            recurse (used,p,counts,i + 1);
                            counts [d]--;
                            used [j] = false;
                        }
                    }
    }
}