# Number of nodes in a B-Tree given approximate degree and number of items to store

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 $$O(N/B^4)$$?