  The index of a Lie algebra is an important algebraic invariant. In 2000,
Vladimir Dergachev and Alexandre Kirillov defined seaweed subalgebras of
$\mathfrak{gl}_n$ (or $\mathfrak{sl}_n$) and provided a formula for the index
of a seaweed algebra using a certain graph, so-called a meander. In a recent
paper, Vincent Coll, Andrew Mayers, and Nick Mayers defined a new statistic for
partitions, namely the index of a partition, which arises from seaweed Lie
algebras of type A. At the end of their paper, they presented an interesting
conjecture, which involves integer partitions into odd parts. Motivated by
their work, in this paper, we exploit various index statistics and the index
weight generating functions for partitions. In particular, we examine their
conjecture by considering the generating function for partitions into odd
parts. We will also reprove another result from their paper using generating
functions.
