  In this paper, we consider sums of class numbers of the type $\sum_{m\equiv
a\pmod{p}} H(4n-m^2)$, where $p$ is an odd prime, $n\in \mathbb{N},$ and $a\in
\mathbb{Z}$. By showing that these are coefficients of mixed mock modular
forms, we obtain explicit formulas. Using these formulas for $p=5$ and $7$, we
then prove a conjecture of Brown et al. in the case that $n=\ell$ is prime.
