We have investigated orbital ordering in the half-doped manganite La_0.5Sr_1.5MnO_4, which displays spin, charge and orbital ordering, by means of unrestricted Hartree-Fock calculations on the multiband p-d model. From recent experiment, it has become clear that La_0.5Sr_1.5MnO_4 exhibits a cross-type (z^2-x^2/y^2-z^2) orbital ordering rather than the widely believed rod-type (3x^2-r^2/3y^2-r^2) orbital ordering. The calculation reveals that cross-type (z^2-x^2/y^2-z^2) orbital ordering results

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... from an effect of in-plane distortion as well as from the relatively long out-of-plane Mn-O distance. For the "Mn^4+" site, it is shown that the elongation along the c-axis of the MnO_6 octahedra leads to an anisotropic charge distribution rather than the isotropic one.