A certain sequence on pure $\kappa-$sparse gapsets

In this paper, we study the pure $\kappa-$sparse gapsets and our focus on getting information about the sequence observed in Table 3 at [1], this sequence is listed in OEIS as A374773. We verify that the cardinality of the set of gapsets with genus $3n+1$ such that the maximum distance between two consecutive elements is $2n$ is equal to the cardinality of the set of gapsets with genus $3n+2$ such that the maximum distance between two consecutive elements is $2n+1$, for all $n\in \mathbb{N}$. In particular, we compute the cardinality of the symmetric and pseudo-symmetric gapsets in these cases.