%I #15 Jan 23 2025 21:57:49

%S 2,3,16,133,1440,22076,401200,8523946,206375088,5611089408,

%T 169259764912,5610386295418,202710195084400,7929759557219228,

%U 333909047017798272,15059194651009154172,724232293050284717248

%N Number of unrooted unlabeled bipartite cubic maps on a compact closed oriented surface with 2*n vertices (and thus 3*n edges).

%C Equivalently, the number of unrooted bicolored triangulations with 2*n triangles (and thus 3*n edges).

%C Equivalently, the number of pairs of permutations (alpha,sigma) up to simultaneous conjugacy on a set of size 3*n with alpha^3=sigma^3=1, acting transitively and without fixed points.

%C There is no recurrence relation known for this sequence.

%H Laura Ciobanu and Alexander Kolpakov, <a href="https://doi.org/10.1016/j.disc.2019.01.014">Free subgroups of free products and combinatorial hypermaps</a>, Discrete Mathematics, 342 (2019), 1415-1433; arXiv:<a href="https://arxiv.org/abs/1708.03842">1708.03842</a> [math.CO], 2017-2019.

%Y Unrooted version of A292187.

%K nonn

%O 1,1

%A _Sasha Kolpakov_, Sep 11 2017

%E Offset edited by _Andrey Zabolotskiy_, Jan 17 2025