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In this study, we perform a numerical simulation on the recently discoveredhigh-temperature superconductor ($T_c$= 73K) Ba$_2$CuO$_{3.2}$ \cite{lietal}while focusing on doping dependence of alternating CuO$_6$ octahedra and CuOchain-like states. Employing the multiband random-phase approximation, wecompute the spin-fluctuation mediated pairing interaction, subsequentlydetermining its pairing eigenvalues and eigenfunctions relative tooxygen-doping levels. We find that, for the certain range of hole doping inBa$_2$CuO$_{3+\delta}$, a singlet $d_{x^2-y^2}$-wave pairing symmetry emergesas long as we keep the doping below the critical value $x_{c}$. Interestinglyupon hole doping, the dominant pairing symmetry undergoes a transition to atriplet (odd paring) type from the singlet state. This change in pairing isdriven by the competition between the nesting vectors coming from the Fermisurface of $d_{z^2}$ and $d_{x^2-y^2}$ orbitals within the CuO$_6$ octahedra.This triplet state is attainable through hole doping, while supressinginter-layer self-doping effects. Furthermore, we present the density of stateswithin the superconducting phase, offering a potential comparison withtunnelling spectra in Ba$_2$CuO$_{3+\delta}$. Our research provides novelinsights into the intricate pairing symmetries in Ba$_2$CuO$_{3+\delta}$ andtheir underlying pairing mechanisms.

Doping induced singlet to triplet superconducting transition in Ba$_{2}$CuO$_{3+\delta}$