  It was shown by Kuperberg that the partition function of the square-ice model
related to half-turn symmetric alternating-sign matrices of even order is the
product of two similar factors. We propose a square-ice model whose states are
in bijection with half-turn symmetric alternating-sign matrices of odd order.
The partition function of the model is expressed via the above mentioned
factors. The contributions to the partition function of the states
corresponding to the alternating-sign matrices having 1 or -1 as the central
entry are found and the related enumerations are obtained.
