  We give a new proof of Milne's formulas for the number of representations of
an integer as a sum of 4m^2 and 4m(m+1) squares. The proof is based on explicit
evaluation of pfaffians with elliptic function entries, and relates Milne's
formulas to Schur Q-polynomials and to correlation functions for continuous
dual Hahn polynomials. We also state a new formula for 2m^2 squares.
