Counting finite algebras in the post varieties

The G-spectrum of a class of algebras is the function that counts, up to isomorphism, the number of at most k-generated algebras in the class, for k = 1, 2,.... We consider the G-spectra of the varieties of algebras generated by a single two-element algebra. We show that such spectra are either polynomial, exponential, or at least doubly exponential as a function of k. For the varieties that have polynomial or exponential G-spectra we provide an exact formula for the function.