  For any integer $m\ge 2$ and a set $V\subset \{1,\dots,m\}$, let $(m,V)$
denote the union of congruence classes of the elements in $V$ modulo $m$. We
study the Hankel determinants for the number of Dyck paths with peaks avoiding
the heights in the set $(m,V)$. For any set $V$ of even elements of an even
modulo $m$, we give an explicit description of the sequence of Hankel
determinants in terms of subsequences of arithmetic progression of integers.
There are numerous instances for varied $(m,V)$ with periodic sequences of
Hankel determinants. We present a sufficient condition for the set $(m,V)$ such
that the sequence of Hankel determinants is periodic, including even and odd
modulus $m$.
