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We derive new fermionic expressions for the characters of the Virasorominimal models $M(k,2k\pm1)$ by analysing the recently introduced half-latticepaths. These fermionic expressions display a quasiparticle formulationcharacteristic of the $\phi_{2,1}$ and $\phi_{1,5}$ integrable perturbations.We find that they arise by imposing a simple restriction on the RSOSquasiparticle states of the unitary models $M(p,p+1)$. In fact, four fermionicexpressions are obtained for each generating function of half-lattice paths offinite length $L$, and these lead to four distinct expressions for mostcharacters $\chi^{k,2k\pm1}_{r,s}$. These are direct analogues of Melzer'sexpressions for $M(p,p+1)$, and their proof entails revisiting, reworking andrefining a proof of Melzer's identities which used combinatorial transforms onlattice paths.  We also derive a bosonic version of the generating functions of length $L$half-lattice paths, this expression being notable in that it involves$q$-trinomial coefficients. Taking the $L\to\infty$ limit shows that thegenerating functions for infinite length half-lattice paths are indeed theVirasoro characters $\chi^{k,2k\pm1}_{r,s}$.

A quartet of fermionic expressions for $M(k,2k\pm1)$ Virasoro characters via half-lattice paths