  Recently, [Phys. Rev. Lett. 130, 221501 (2023)] Jacobson and Visser
calculated the quantum partition function of a fixed, finite volume of a region
with the topology of a ball in the saddle point approximation within the
context of Einstein's gravity with or without a cosmological constant. The
result can be interpreted as the dimension of Hilbert space of the theory. Here
we extend their computation to a theory defined in principle with infinitely
many powers of curvature in three dimensions. We confirm their result: The
partition function of a spatial region in the leading saddle point
approximation is given as the exponential of the Bekenstein-Hawking or the Wald
entropy of the boundary of the finite spatial region both in the case of zero
and finite cosmological constant. In the latter case, the effective Newton's
constant appears in the entropy formula. The calculations lend support to the
holographic nature of gravity for finite regions of space with a boundary.
