Hypernested Block Hyper Notation (HBHN) is the 6th part of HN.

Rules

An expression is of the form H<n,A>, where n is the base and A is an array.

1. If there is no array, H<n> = n^n
2. If the array's first entry is 1, delete it.
3. If the array is a sequence array, decrease it by one, then nest the whole expression into the base n times.
4. If the array is a limit array, change the array into the nth member of it's FS.

Arrays

As always, definitions from NBHN apply here.

There are not much changes in the definition, but there is a big change in the growth rate.

We need to introduce a new block, called [X]. X is the biggest array, but only in HBHN. (X is also a cascader, but more on that in the next parts)

To solve A,[X],B, you just solve it like you would solve A,[B],B, except when A is 1 and B is a sequence array, then the FS can be calculated as follows:

First, take the WHOLE array (unless [X] is inside a block, then take the whole array inside of the block), and call it N.

Then, go back to 1,[X],B. Decrease B by 1, and this is the first member of the FS, which we will call FS(1). The second member of the FS, which we will call FS(2), will be 1,[N],[X],B-1. The (n+1)th member of the FS, which we will call FS(n+1), will be 1,[FS(n)],[X],B-1.

That's it.