  We construct an equation of state for Quantum Chromodynamics (QCD) at finite
temperature and chemical potentials for baryon number $B$, electric charge $Q$
and strangeness $S$. We use the Taylor expansion method, up to the fourth power
for the chemical potentials. This requires the knowledge of all diagonal and
non-diagonal $BQS$ correlators up to fourth order: these results recently
became available from lattice QCD simulations, albeit only at a finite lattice
spacing $N_t=12$. We smoothly merge these results to the Hadron Resonance Gas
(HRG) model, to be able to reach temperatures as low as 30 MeV; in the high
temperature regime, we impose a smooth approach to the Stefan-Boltzmann limit.
We provide a parameterization for each one of these $BQS$ correlators as
functions of the temperature. We then calculate pressure, energy density,
entropy density, baryonic, strangeness, electric charge densities and compare
the two cases of strangeness neutrality and $\mu_S=\mu_Q=0$. We also calculate
the isentropic trajectories and compare them in the two cases. Our equation of
state can be readily used as an input of hydrodynamical simulations of matter
created at the Relativistic Heavy Ion Collider (RHIC).
