A292206 Number of unrooted unlabeled connected four-regular maps on a compact closed oriented surface with n vertices (and thus 2*n edges).

2, 7, 36, 365, 5250, 103801, 2492164, 70304018, 2265110191, 82013270998, 3295691020635, 145553281837454, 7008046130978980, 365354356543414133, 20504381826687810441, 1232562762503125498772, 79012106044626365750974

Offset

0,1

Comments

Equivalently, the number of unrooted quadrangulations of oriented surfaces with n quadrangles (and thus 2*n edges).

Equivalently, the number of pairs of permutations (alpha,sigma) up to simultaneous conjugacy on a set of size 4*n with alpha^2=sigma^4=1, acting transitively and without fixed points.

There is no recurrence relation known for this sequence.

Links

Table of n, a(n) for n=0..16.

L. Ciobanu, A. Kolpakov, Free subgroups of free products and combinatorial hypermaps, arXiv:1708.03842 [math.CO], 2017.

Crossrefs

Unrooted version of A292186.

Sequence in context: A007474 A002724 A348106 * A203900 A209251 A366670

Adjacent sequences: A292203 A292204 A292205 * A292207 A292208 A292209

Keyword

nonn

Author

Sasha Kolpakov, Sep 11 2017

Status

approved