A trivalent tree, also called a 3-valent tree, is a tree for which each node has vertex
degree 
.
The numbers of trivalent trees on 
, 2, ... nodes, counted up
to graph isomorphism, are 1, 1, 1, 2, 2, 4,
6, 11, 18, 37, 66, 135, 265, 552, ... (OEIS A000672).
The numbers of 3-Cayley trees, which have vertex degree either 1 or 3, on 
, 2, ... nodes, including
the one-node tree by convention
and counted up to graph isomorphism, are 1,
1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 2, 0, 4, ... (OEIS A052120).
These are sometimes called boron trees, since such a tree
with 
nodes has 
nodes of vertex
degree 3 (corresponding to boron atoms) and 
nodes of vertex
degree 1 (corresponding to hydrogen atoms) for 
, 4, ....
