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%I #11 Sep 17 2017 03:58:00
%S 2,3,16,133,1440,22076,401200,8523946,206375088,5611089408,
%T 169259764912,5610386295418,202710195084400,7929759557219228,
%U 333909047017798272,15059194651009154172,724232293050284717248
%N Number of unrooted unlabelled 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 L. Ciobanu, A. Kolpakov, <a href="https://arxiv.org/abs/1708.03842">Free subgroups of free products and combinatorial hypermaps</a>, arXiv:1708.03842 [math.CO], 2017.
%Y Unrooted version of A292187.
%K nonn
%O 0,1
%A _Sasha Kolpakov_, Sep 11 2017