  We work with lattice walks in $\mathbb{Z}^{r+1}$ using step set $\{\pm
1\}^{r+1}$ that finish with $x_{r+1} = 0$. We further impose conditions of
avoiding backtracking (i.e. $[v,-v]$) and avoiding consecutive steps (i.e.
$[v,v]$) each possibly combined with restricting to the half-space $x_{r+1}
\geq 0$. We find in all cases the generating functions for such walks are
algebraic and give explicit formulas for them. We also find polynomial
recurrences for their coefficients. From the generating functions we find the
asymptotic enumeration of each family of walks considered. The enumeration in
special cases includes central binomial coefficients and Catalan numbers as
well as relations to enumeration of another family of walks previously studied
for which we provide bijection.
