A292207 - OEIS

A292207

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

2, 3, 16, 133, 1440, 22076, 401200, 8523946, 206375088, 5611089408, 169259764912, 5610386295418, 202710195084400, 7929759557219228, 333909047017798272, 15059194651009154172, 724232293050284717248

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

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

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.

There is no recurrence relation known for this sequence.

LINKS

Table of n, a(n) for n=1..17.

Laura Ciobanu and Alexander Kolpakov, Free subgroups of free products and combinatorial hypermaps, Discrete Mathematics, 342 (2019), 1415-1433; arXiv:1708.03842 [math.CO], 2017-2019.

CROSSREFS

Unrooted version of A292187.

Sequence in context: A370201 A356882 A139802 * A063666 A006247 A052318

Adjacent sequences: A292204 A292205 A292206 * A292208 A292209 A292210

KEYWORD

nonn

AUTHOR

Sasha Kolpakov, Sep 11 2017

EXTENSIONS

Offset edited by Andrey Zabolotskiy, Jan 17 2025

STATUS

approved