  We consider the anisotropic Ising model on the triangular lattice with finite
boundaries, and use Kaufman's spinor method to calculate low-temperature series
expansions for the partition function to high order. From these we can obtain
108-term series expansions for the bulk, surface and corner free energies. We
extrapolate these to all terms and thereby conjecture the exact results for
each. Our results agree with the exactly known bulk free energy. For the
isotropic case, they also agree with Vernier and Jacobsen's conjecture for the
$60^{\circ}$ corners, and with Cardy and Peschel's conformal invariance
predictions for the dominant behaviour at criticality.
