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We consider the extended discrete KP hierarchy and show that similarityreduction of its subhierarchies lead to purely discrete equations withdependence on some number of parameters together with equations governingdeformations with respect to these parameters. It is written down discreteequations which naturally generalize the first discrete Painlev\'e equation$\mathrm{dP}_{\rm I}$ in a sense that autonomous version of these equationsadmit the limit to the first Painlev\'e equation. It is shown that each ofthese equations describes B\"acklund transformations of Veselov-Shabat periodicdressing lattices with odd period known also as Noumi-Yamada systems of type$A_{2(n-1)}^{(1)}$.

Integrable Discrete Equations Derived by Similarity Reduction of the Extended Discrete KP Hierarchy