  If $\mathfrak{g}$ is a Frobenius Lie algebra, then the spectrum of
$\mathfrak{g}$ is an algebraic invariant equal to the multiset of eigenvalues
corresponding to a particular operator acting on $\mathfrak{g}$. In the case of
Frobenius seaweed subalgebras of $A_{n-1}=\mathfrak{sl}(n)$, or type-A seaweeds
for short, it has been shown that the spectrum can be computed combinatorially
using an attendant graph. With the aid of such graphs, it was further shown
that the spectrum of a type-A seaweed consists of an unbroken sequence of
integers centered at $\frac{1}{2}$. It has been conjectured that if the
eigenvalues are arranged in increasing order, then the sequence of
multiplicities forms a unimodal sequence about $\frac{1}{2}$. Here, we
establish this conjecture for certain families of Frobenius type-A seaweeds by
finding explicit formulas for their spectra; in fact, for some families we are
able to show that the corresponding sequences of multiplicities form
log-concave sequences. All arguments are combinatorial.
