  We consider the sum of the Einstein-Hilbert action and a Pontryagin density
(PD) in arbitrary even dimension $D$. All curvatures are functions of
independent affine (torsionless) connections only. In arbitrary dimension, not
only in $D=4n$, these first order PD terms are shown to be covariant
divergences of "Chern-Simons" currents. The field equation for the connection
leads to it being Levi-Civita, and to the metric and affine field equations
being equivalent to the second order metric theory. This result is a
counterexample to the theorem stating that purely metric and metric-affine
models can only be equivalent for Lovelock theories.
