  We study extended Hubbard model on a triangular lattice near doping $x=1/3$,
which may be relevant for the recently discovered superconductor Na$_x$CoO$_2
\cdot y$H$_2$O. By generalizing this model to $N$ fermionic species, we
formulate a meanfield description in the limit of large $N$. In meanfield, we
find two possible phases: a renormalized Fermi liquid and a $\rt3rt3$ charge
density wave state. The transition between the two phases is driven by
increasing the nearest neighbor repulsion and is found to be first order for
doping $x=1/3$, but occurs close to the point of the local instability of the
uniform liquid. We also study fluctuations about the uniform meanfield state in
a systematic 1/N expansion, focusing on the residual interaction of
quasiparticles and possible superconducting instabilities due to this
interaction. Upon moving towards the CDW instability, the increasing charge
fluctuations favor a particular $f$-wave triplet state. (This state was
recently discussed by Tanakaet al, cond-mat/0311266). We also report a direct
Gutzwiller wavefunction study of the spin-1/2 model.
