  We consider a class of parity even, six-derivative gravity theories in three
dimensions. After linearizing around anti-de Sitter space, the theories have
one massless and two massive graviton solutions for generic values of the
parameters. At a special, so-called tricritical, point in parameter space the
two massive graviton solutions become massless and they are replaced by two
solutions with logarithmic and logarithmic-squared boundary behavior. The
theory at this point is conjectured to be dual to a rank-3 Logarithmic
Conformal Field Theory (LCFT) whose boundary stress tensor, central charges and
new anomaly we calculate. We also calculate the conserved Abbott-Deser-Tekin
charges. At the tricritical point, these vanish for excitations that obey
Brown-Henneaux and logarithmic boundary conditions, while they are generically
non-zero for excitations that show logarithmic-squared boundary behavior. This
suggests that a truncation of the tricritical gravity theory and its
corresponding dual LCFT can be realized either via boundary conditions on the
allowed gravitational excitations, or via restriction to a zero charge
sub-sector. We comment on the structure of the truncated theory.
