If we have a tree with M nodes and this tree have N leaf nodes, this tree have M - N + 1 nodes without right child in its corresponding binary tree.
Proof:
In Binary tree, we consider 4 kinds of nodes: With both children (i.e. n2), with left child but no right child (set as x), with right child but no left child (set as y), without children (i.e., n0). Based on property of binary tree, n2 = n0 - 1. So, M can be shown as: M = x + y + 2n0 - 1;
Because leaf nodes in the tree will have no left child in corresponding binary tree. So, y + n0 = N; While, the number of nodes without right child in its corresponding binary tree is: x + n0; Thus, the answer is: x + n0 = M - (y + n0) + 1 = M - N + 1.