I’m trying to solve a problem involving binary trees where I need to count the number of subtrees that can be formed with each node as the center and a given radius
????
R. The subtrees are considered identical if their structures are the same, even if they appear multiple times within the tree. Here’s the detailed problem:

Problem:
Given a binary tree, determine the number of unique subtrees that can be formed with each node as the center and radius
????
R.

Definitions:

Binary Tree: A tree in which each node has at most two children.
Radius
????
R: The maximum distance from the center node to any other node in the subtree.

Example:
Consider this binary tree:

 1
/ 

2 3
/
4 5

For
????

1
R=1:

Center at 1: Subtree
[1,2,3]
Center at 2: Subtree
[2,4,5]
Center at 3: Subtree
[3]
Center at 4: Subtree
[4]
Center at 5: Subtree
[5]
Each subtree is unique in structure.