A strongly binary tree is a rooted tree for which the root is adjacent to either zero or two vertices, and all non-root vertices are adjacent to either one or three vertices. The numbers of strongly binary trees on n = 1, 2, ... nodes are 1, 0, 1, 0, 1, 0, 2, 0, 3, 0, 6, 0, ... (OEIS A001190). The counts are 0 for n even, and g_k for odd n = 2k + 1, where g_n is the number of weakly binary trees on n nodes.

binary tree | complete binary tree | rooted tree | weakly binary tree