  The orbital shapes and charge disproportionations at nominal Mn$^{3+}$ and
Mn$^{4+}$ sites for the charge- and orbital-ordered phases have been studied on
half-doped manganites Pr(Sr$_{0.1}$Ca$_{0.9}$)$_2$Mn$_2$O$_7$ and
Eu$_{0.5}$Ca$_{1.5}$MnO$_4$ with double-layer and single-layer Mn-O networks,
respectively, by means of x-ray structural analyses, in comparison with
Pr$_{0.5}$Ca$_{0.5}$MnO$_3$ with the pseudo cubic network. In a single-layer
Eu$_{0.5}$Ca$_{1.5}$MnO$_4$ system, the ($y^2-z^2$)/($z^2-x^2$)-type orbital
shape is observed, while the ($3y^2-r^2$)/($3x^2-r^2$)-type orbital shape in a
pseudo cubic Pr$_{0.5}$Ca$_{0.5}$MnO$_3$ system. In a double-layer
Pr(Sr$_{0.1}$Ca$_{0.9}$)$_2$Mn$_2$O$_7$ system, the orbital shape is found to
undergo a large change upon thermally induced rotation of orbital stripe.
Furthermore, clear charge disproportionation is observed for the pseudo cubic
and double-layer systems, while not in the single-layer system. These results
indicate that the orbital shape and charge disproportionation are sensitive to
the dimension of Mn-O network.
