cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A129114 Number of unrooted unlabeled connected triangular maps on a compact closed oriented surface with 2n faces (and thus 3n edges).

Original entry on oeis.org

1, 3, 11, 81, 1228, 28174, 843186, 30551755, 1291861997, 62352938720, 3381736322813, 203604398647922, 13475238697911184, 972429507963453210, 75993857157285258473, 6393779463050776636807, 576237114190853665462712, 55385308766655472416299110, 5655262782600929403228668176
Offset: 0

Views

Author

Samuel A. Vidal, Mar 30 2007

Keywords

Comments

Equivalently, the number of pairs of permutations (sigma,tau) up to simultaneous conjugacy on a set of size 6*n with sigma^3=tau^2=1, acting transitively and with no fixed point.

Crossrefs

Column 3 of A380626.
Connected version of A129115.
Unrooted version of A062980.
Cf. also A121350, A121352, A005133.

Formula

Inverse Euler transform of A129115. - Andrew Howroyd, Jan 29 2025

Extensions

a(0)=1 prepended and terms a(17) onwards from Andrew Howroyd, Jan 29 2025

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

Original entry on oeis.org

1, 2, 7, 36, 365, 5250, 103801, 2492164, 70304018, 2265110191, 82013270998, 3295691020635, 145553281837454, 7008046130978980, 365354356543414133, 20504381826687810441, 1232562762503125498772, 79012106044626365750974, 5380476164948914549410335, 387882486153123498708054879
Offset: 0

Views

Author

Sasha Kolpakov, Sep 11 2017

Keywords

Comments

Equivalently, the number of unrooted quadrangulations of oriented surfaces with n quadrangles (and thus 2*n edges).
Equivalently, the number of pairs (alpha,sigma) of permutations on a set of size 4*n up to simultaneous conjugacy such that alpha (resp. sigma) has only cycles of length 2 (resp. 4) and the subgroup generated by them acts transitively.

Examples

			For n = 1, a(n) = 2:
1) the figure-eight map on a sphere (1 vertex, which has degree 4, and 2 edges) <-> its dual map, which is the quadrangulation of a sphere created by a 2-edge path (it bounds 1 region, which has 4 boundary segments, even though they are formed by only 2 different edges) <-> the conjugacy class of the pair of permutations ((12)(34), (1234));
2) the map on a torus consisting of two non-homotopic nontrivial loops (1 vertex, which has degree 4, and 2 edges) <-> its dual map, which is the same map again (it bounds 1 region, which has 4 boundary segments, even though they are formed by only 2 different edges) <-> the conjugacy class of the pair of permutations ((13)(24), (1234)).
		

Crossrefs

Column 4 of A380626.
Unrooted version of A292186.
Cf. A268556.

Formula

Inverse Euler transform of A268556. - Andrew Howroyd, Jan 29 2025

Extensions

Edited by Andrey Zabolotskiy, Jan 17 2025
a(0)=1 prepended and a(18) onwards from Andrew Howroyd, Jan 29 2025

A380627 Number of sensed 5-regular combinatorial maps with 2n vertices.

Original entry on oeis.org

1, 29, 44106, 549530780, 20295421909475, 1648575609240648557, 249793950749168438672432, 63401746172946552016801544036, 24987461004098373175802500801970565, 14453024762638492834399423828614955417596, 11746112443686354689351672116979783313870949792
Offset: 0

Views

Author

Andrew Howroyd, Jan 29 2025

Keywords

Comments

There are no 5-regular combinatorial maps with an odd number of vertices.

Crossrefs

With interspersed zeros column 5 of A380626.
Cf. A380623 (rooted).

A380628 Number of sensed 6-regular combinatorial maps with n vertices.

Original entry on oeis.org

1, 5, 174, 26614, 10107019, 6605320523, 6579728772912, 9276594775469270, 17585361213957551946, 43146230949730084319048, 133038707207639820811320335, 503600964942920889570482778054, 2296079661132313737232568593302086, 12410968049799470734493011986934972606
Offset: 0

Views

Author

Andrew Howroyd, Jan 29 2025

Keywords

Crossrefs

Column 6 of A380626.
Cf. A380624 (rooted).

A380629 Number of sensed regular combinatorial maps with n edges.

Original entry on oeis.org

1, 2, 3, 9, 26, 135, 1124, 11225, 143600, 2156862, 36069006, 681844857, 14387370477, 327462904319, 8171705457024, 221137571070305, 6373582250114091, 197210862517274355, 6521583445100185049, 227168823675390365225, 8396976723995537706278, 327880018217851412105973
Offset: 0

Views

Author

Andrew Howroyd, Jan 29 2025

Keywords

Crossrefs

Cf. A170946, A380625 (rooted), A380626.

Programs

  • PARI
    a(n)={if(n==0, 1, sumdiv(2*n, d, T(d,2*n/d)))} \\ T(n,k) defined in A380622.

Formula

a(n) = Sum_{d|2*n} A380626(d,2*n/d) for n > 0.
Showing 1-5 of 5 results.