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 (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 is the number of weakly
binary trees on
nodes (Finch 2003, p. 298).
Finch, S. R. Mathematical Constants. Cambridge, England: Cambridge University Press, 2003.Sloane,
N. J. A. Sequence A001190/M0790
in "The On-Line Encyclopedia of Integer Sequences."
, 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 
is the number of weakly
binary trees on 
nodes (Finch 2003, p. 298).
