  For every $m \in {\C} \setminus \{0, -2\}$ and every nonnegative integer $k$
we define the vertex operator (super)algebra $D_{m,k}$ having two generators
and rank $ \frac{3 m}{m + 2}$. If $m$ is a positive integer then $D_{m,k}$ can
be realized as a subalgebra of a lattice vertex algebra. In this case, we prove
that $D_{m,k}$ is a regular vertex operator (super)algebra and find the number
of inequivalent irreducible modules.
