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
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
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)).
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
With interspersed zeros column 5 of
A380626.
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
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
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a(n)={if(n==0, 1, sumdiv(2*n, d, T(d,2*n/d)))} \\ T(n,k) defined in A380622.
Showing 1-5 of 5 results.
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