In this study, we perform a numerical simulation on the recently discovered
high-temperature superconductor (Tcβ= 73K) Ba2βCuO3.2β \cite{lietal}
while focusing on doping dependence of alternating CuO6β octahedra and CuO
chain-like states. Employing the multiband random-phase approximation, we
compute the spin-fluctuation mediated pairing interaction, subsequently
determining its pairing eigenvalues and eigenfunctions relative to
oxygen-doping levels. We find that, for the certain range of hole doping in
Ba2βCuO3+Ξ΄β, a singlet dx2βy2β-wave pairing symmetry emerges
as long as we keep the doping below the critical value xcβ. Interestingly
upon hole doping, the dominant pairing symmetry undergoes a transition to a
triplet (odd paring) type from the singlet state. This change in pairing is
driven by the competition between the nesting vectors coming from the Fermi
surface of dz2β and dx2βy2β orbitals within the CuO6β octahedra.
This triplet state is attainable through hole doping, while supressing
inter-layer self-doping effects. Furthermore, we present the density of states
within the superconducting phase, offering a potential comparison with
tunnelling spectra in Ba2βCuO3+Ξ΄β. Our research provides novel
insights into the intricate pairing symmetries in Ba2βCuO3+Ξ΄β and
their underlying pairing mechanisms