Block Array Hyper Notation (BaHN) is the 4th part of Hyper Notation.

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

Now, we introduce a different type of array: the arrays of the form A,[x],B, where A and B are arrays. [x] is called a block, and x is the number inside of [x]. And the definitions from LHN still apply.

Now, how do we calculate the FS of these new types of arrays?

First, look at A, then calculate the FS of A, and then, make a copy of that FS, call it FS(A). Then, add '',[x],B'' at the end of each of the members of FS(A), and then, FS(A) is the FS of A,[x],B.

Except if A is 1, then we need to look at B.

If B is a limit array, calculate the FS of B, make a copy of that FS, call it FS(B), add ''[x],'' at the start of each of the members of FS(B), and then, FS(B) is the FS of A,[x],B.

If B is a sequence array, decrease B by 1, and this is the first member of the FS. Then, to get to a member of the FS to the next one, add ''[x-1],'' at the start of the array. (Unless x is 1, then replace the number of the entry at the left of [x] by 1,2)

Finally, if A doesn't appear on A,[x],B, that means A is 1, and if B doesn't appear, that means B is 1. And if A and/or B are 1, then you can delete them.

Edit 1: To fix errors in some arrays, the [x] in A,[x],B will be the block with the highest number inside of it (call this block []), and if there are multiple []s, then it's the left-most [].

Edit 2: When B is 0, remove B and [x] from the array.