Column 2 of Marshall table, p. 443. A143094 is the analogous enumeration, column 3 of Marshall table, if we view the K-structures just as graded rings.

REFERENCES

Ido Efrat, Valuations, orderings and Milnor K-theory, Mathematical Surveys and Monographs, vol. 124, American Mathematical Society, 2006.

Murray Marshall, Book Review: Valuations, orderings and Milnor K-theory, by Ido Efrat, Bulletin of the American Mathematical Society, Vol. 45 (July 2008) No. 3, pp. 439-444.

a(n) = the number of nonisomorphic elementary types K_*(F)/S with |F^X/S| = 2^n, if we view the K-structures as graded rings with distinguished element.