  We present a model of holographic dark energy in which the Infrared cutoff is
determined by both the Ricci and the Gauss-Bonnet invariants. Such a
construction has the significant advantage that the Infrared cutoff, and
consequently the holographic dark energy density, does not depend on the future
or the past evolution of the universe, but only on its current features, and
moreover it is determined by invariants, whose role is fundamental in
gravitational theories. We extract analytical solutions for the behavior of the
dark energy density and equation-of-state parameters as functions of the
redshift. These reveal the usual thermal history of the universe, with the
sequence of radiation, matter and dark energy epochs, resulting in the future
to a complete dark energy domination. The corresponding dark energy
equation-of-state parameter can lie in the quintessence or phantom regime, or
experience the phantom-divide crossing during the cosmological evolution, and
its asymptotic value can be quintessence-like, phantom-like, or be exactly
equal to the cosmological-constant value. Finally, we extract the constraints
on the model parameters that arise from Big Bang Nucleosynthesis.
