Alternate derivation of the Ginocchio--Haxton relation [(2j-3)/6]

We have found an alternate way of deriving the Ginocchio-Haxton relation [(2j-3)/6], where the square brackets mean the largest integer that is less than or equal to what is inside them. Our derivation involves the calculation of the number of states with total angular momentum J=j for 3 identical particles (e.g., neutrons) in a j-shell.