  We compute the Heegaard Floer homology of any rational homology 3-sphere with
an open book decomposition of the form (T,\phi), where T is a genus one surface
with one boundary component. In addition, we compute the Heegaard Floer
homology of any T^2-bundle over S^1 with first Betti number equal to one, and
we compare our results with those of Lebow on the embedded contact homology of
such torus bundles. We use these computations to place restrictions on
Stein-filllings of the contact structures compatible with such open books, to
narrow down somewhat the class of 3-braid knots with finite concordance order,
and to identify all quasi-alternating links with braid index at most 3.
