A formula for computing (1,2,3)-inverses of g-circulants

Recent work on generalized inverses of linear operators centres around the construction of efficient algorithms for their computation. Here invariably structural properties of the operators and matrices involved are very convenient. As a contribution we obtain a rapidly evaluable explicit expression for (1, 2, 3)-inverses of singular g-circulants that originate in a nonsingular 1-circulant.