  We consider the most general higher order corrections to the pure gravity
action in $D$ dimensions constructed from the basis of the curvature monomial
invariants of order 4 and 6, and degree 2 and 3, respectively. Perturbatively
solving the resulting sixth-order equations we analyze the influence of the
corrections upon a static and spherically symmetric back hole. Treating the
total mass of the system as the boundary condition we calculate location of the
event horizon, modifications to its temperature and the entropy. The entropy is
calculated by integrating the local geometric term constructed from the
derivative of the Lagrangian with respect to the Riemann tensor over a
spacelike section of the event horizon. It is demonstrated that identical
result can be obtained by integration of the first law of the black hole
thermodynamics with a suitable choice of the integration constant. We show that
reducing coefficients to the Lovelock combination, the approximate expression
describing entropy becomes exact. Finally, we briefly discuss the problem of
field redefinition and analyze consequences of a different choice of the
boundary conditions in which the integration constant is related to the exact
location of the event horizon and thus to the horizon defined mass.
