In Fredman and Willards paper “Surpassing the Information Theoretic Bound with Fusion Trees” They mention that the number of nodes in a B-Tree is $ O(N/B^4)$ , where $ N$ is the number of keys they store in the tree, and $ B$ is the approximate degree.

I am not quite sure how they got this result, reading the original paper on B-Trees, Bayer and McCreight only mention a bound for a tree with height $ h$ , and approximate degree $ B$ , however not one for the number of keys to store. They give the following bound where $ N(T)$ is the number of nodes in a tree $ T\in\tau(B,h)$ . (approximate degree $ B$ and height $ h$ ) $ $ 1+\frac{2}{B}((B+1)^{h-1}-1)\leq N(T)\leq \frac{1}{2B}((2B+1)^h-1)$ $ Is there any way i could go from this, to Fredman and Willards $ O(N/B^4)$ ?