I am attempting to find a formula that describes the number of leaf nodes in a full binary tree of depth
k, therefore nodes at a depth
<k have exactly two children and the leaves are at depth K.
This gives me the following pattern.
A tree with 1 Node has 1 Leaf
A tree with 3 Nodes has 2 leaves
A tree with 7 Nodes has 4 leaves
A tree with 15 Nodes has 8 leaves
A tree with 31 Nodes has 16 leaves
I am trying to figure out a formula that tells the number of leaves given
N = Number of Nodes but have not been able to figure it out