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Atomic structure and electronic band structure are fundamental properties for understanding the mechanism of superconductivity. Motivated by the discovery of pressure-induced high-temperature superconductivity at 80 K in the bilayer Rud-dlesden-Popper nickelate La3Ni2O7, the atomic structure and electronic band structure of the trilayer nickelate La4Ni3O10 under pressure up to 44.3 GPa are investigated. A structural transition from the monoclinic P21/a space group to the tetragonal I4/mmm around 12.6–13.4 GPa is identified, accompanied by a drop of resistance below 7 K. Density functional theory calculations suggest that the bonding state of Ni 3 d z 2 orbital rises and crosses the Fermi level at high pressures, which may give rise to possible superconductivity observed in resistance under pressure in La4Ni3O10. The trilayer nickelate La4Ni3O10 shows some similarities with the bilayer La3Ni2O7 and has unique properties, providing a new platform to investigate the underlying mechanism of superconductivity in nickelates. [ABSTRACT FROM AUTHOR]