A strongly binary tree is a rooted tree for which the root vertex is adjacent
to either zero or two vertices, and all non-root
vertices are adjacent
to either one or three vertices (Finch 2003, p. 298).
The numbers of strongly binary trees on 
, 2, ... nodes are 1, 0,
1, 0, 1, 0, 2, 0, 3, 0, 6, 0, ... (OEIS A001190).
The counts are 0 for 
even, and 
for odd 
, where 
and 
is the number of weakly
binary trees on 
nodes, including the degenerate one-vertex weakly binary
tree.
