I am studying Fractal Merkle Tree Traversal algorithm in the book “Post Quantum Cryptography” (PDF). On the [pag. 54] I don't understand this paragraph:
We may determine the number of pebbles returned at these times by observing that a leaf is returned every single round, a pebble at height $ih + 1$ every two rounds, one at height $ih + 2$ every four rounds, etc.
Now, please look at Figure 4.1 of “Merkle-Tree Traversal Techniques” (PDF):
In round 1 is true that leaf $n_0$ no longer needed. Now in paragraph says "pebble at height $ih + 1$ every two rounds, ... " then for the second round, in the case of $i = 1$ and $h = 1$, we see that in the height $i*h+1=2$ should have a node that is no longer required. Which would be in this example that node?
Also, can someone explain the meaning of $A$ in the equation on page 55? $$A+[A/2]+[A/4]+\cdots+[A/2^h] $$