  For p \in {3, 4} and all p' > p, with p' coprime to p, we obtain fermionic
expressions for the combination \chi^{p, p'}_{1, s} + q^{\Delta} \chi^{p,
p'}_{p-1,s} of Virasoro (W_2) characters for various values of s, and
particular choices of Delta. Equating these expressions with known product
expressions, we obtain q-series identities which are akin to the Andrews-Gordon
identities. For p=3, these identities were conjectured by Bytsko. For p=4, we
obtain identities whose form is a variation on that of the p=3 cases. These
identities appear to be new.
  The case (p,p')=(3,14) is particularly interesting because it relates not
only to W_2, but also to W_3 characters, and offers W_3 analogues of the
original Andrews-Gordon identities. Our fermionic expressions for these
characters differ from those of Andrews et al which involve Gaussian
polynomials.
