  We present in this paper empirical formulas for the number of angular
momentum I states for three and four identical fermions or bosons. In the cases
with large I we prove that the number of states with the same ${\cal M}$ and n
but different J is identical if $I \ge (n-2)J - {1/2} (n-1)(n-2)$ for fermions
and $I \ge (n-2)J$ for bosons, and that the number of states is also identical
for the same ${\cal M}$ but different n and J if ${\cal M} \le $min(n, 2J+1 -
n) for fermions and for ${\cal M} \le $min(n, 2J) for bosons. Here ${\cal M}
=I_{max}-I$, n is the particle number, and J refers to the angular momentum of
a single-particle orbit for fermions, or the spin L carried by bosons.
