  We present a series of Darboux integrable discrete equations on the square
lattice. Equations of the series are numbered with natural numbers $M$. All the
equations have a first integral of the first order in one of directions of the
two-dimensional lattice. The minimal order of a first integral in the other
direction is equal to $3M$ for an equation with the number $M$.
  In the cases $M=1,\ 2,\ 3$ we show that those equations are integrable in
quadratures. More precisely, we construct their general solutions in terms of
the discrete integrals.
  We also construct a modified series of Darboux integrable discrete equations
which have in different directions the first integrals of the orders $2$ and
$3M-1$, where $M$ is the equation number in series. Both first integrals are
unobvious in this case.
