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Vacuum spacetimes admitting a non-twisting geodetic multiple Weyl alignednull direction (WAND) are analyzed in arbitrary dimension using recentlydeveloped higher-dimensional Newman-Penrose (NP) formalism. We determinedependence of the metric and of the Weyl tensor on the affine parameter r alongnull geodesics generated by the WAND for type III and N spacetimes and for aspecial class of type II and D spacetimes, containing e.g.Schwarzschild-Tangherlini black holes and black strings and branes.  For types III and N, all metric components are at most quadratic polynomialsin r while for types II and D the r-dependence of the metric as well as of theWeyl tensor is determined by an integer m corresponding to the rank of theexpansion matrix S_{ij}. It is shown that for non-vanishing expansion, allthese spacetimes contain a curvature singularity.  As an illustrative example, a shearing expanding type N five-dimensionalvacuum solution is also re-derived using higher-dimensional NP formalism. Thissolution can be, however, identified with a direct product of a knownfour-dimensional type N metric with an extra dimension.

Newman-Penrose formalism in higher dimensions: vacuum spacetimes with a non-twisting geodetic multiple Weyl aligned null direction