Java Number Pattern Recursion

So you need to write a recursive function. Something of this form:

private String pattern(int num) {
    // ...
}

The most important part is finding the right exit condition that should stop the recursion. In this case, that's when num == 1.

From the description, it looks like for a number k, the output is pattern(k - 1) + k + pattern(k - 1).

I already spoiled too much. You might need to improve the efficiency of this. For example, realize that you don't need to run pattern(k - 1) twice, it's enough to do it once.

I'm a little stuck on what the number pattern is to be able to complete this problem.

Lets try to analyse the sequence using some function f
f(1) = 1 (Total digits = 1)
f(2) = 1 2 1 ( Total digits = 3)
f(3) = 121 3 121 (Total digits = 7)
f(4) = 1213121 4 1213121 (Total digits = 15)
f(5) = 121312141213121 5 121312141213121 (Total digits = 31)

So as you can observe total digits sequence looks like 1,3,7,15,31,....2^n-1
Now we can express this logic as mentioned below(Note : in order to help you to better understand how the program works i am printing sequence at every level)

public class SequenceGenerator {
    public static void main(String[] args) {
        generate(7);
    }

    static void generate(int depth) {
        recursiveGenerator(1, null, depth);
    }

    static void recursiveGenerator(int num, String prev, int limit) {
        if (num <= limit) {
            if (prev != null) {
                System.out.println();
            }
            if (prev != null) {
                System.out.printf("%s %d %s", prev, num, prev);

            } else {
                prev = "";
                System.out.printf("%d", num);
            }
            if (prev.equals("")) {
                prev += num + prev;
            } else {
                prev += " " + num + " " + prev;
            }
            recursiveGenerator(++num, prev, limit);
        }
    }
}

Outputs

1
1 2 1
1 2 1 3 1 2 1
1 2 1 3 1 2 1 4 1 2 1 3 1 2 1
1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 5 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1
1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 5 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 6 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 5 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1
1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 5 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 6 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 5 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 7 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 5 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 6 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 5 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1