  In this work, new recursion relations for the number of spin-J states for
identical particles in a single-j shell are presented. Such relations are
obtained using the generating-function technique, which enables one to exhibit
an odd-even staggering in the spin distribution of an even number of fermions
in a single-j shell: the number of states with an even value of J is larger
than the number of states with an odd value of J. An analytical expression of
the excess of states with an even value of J is provided, and its asymptotic
behavior for large values of j is discussed.
