  Let F be a finite field of characteristic 2 and h be the element x^3+y^3+xyz
of F[[x,y,z]]. In an earlier paper we made a precise conjecture as to the
values of the colengths of the ideals (x^q,y^q,z^q,h^j) for q a power of 2. We
also showed that if the conjecture holds then the Hilbert-Kunz series of H=uv+h
is algebraic (of degree 2) over Q(w), and that mu(h) is algebraic (explicitly,
(4/3)+(5/14)sqrt(7)). In this note, assuming the same conjecture, we use a
theory of infinite matrices to rederive this result, and we extend it to a
wider class of H; for example H=g(u,v)+h. In a follow-up paper, under the same
hypothesis, we will show that transcendental Hilbert-Kunz multiplicities exist.
