A379439 -id:A379439 - cp's OEIS frontend

A348800 a(n) = number of unsensed genus 7 maps with n edges.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 254118439668, 52148049818864, 5634797561708385, 426497331688178676, 25388940147173859412, 1265623233919838264624, 54940200059090328012148

Offset: 0

Michael De Vlieger, Nov 01 2021

nonn

Evgeniy Krasko and Alexander Omelchenko, Enumeration of Unsensed Orientable Maps on Surfaces of a Given Genus, arXiv:1712.10139 [math.CO], 2017, see Appendix Table 3.

Column k=7 of A379439.
Cf. A238357 (rooted), A239921 (sensed).
Cf. A006387, A214814, A214815, A297880, A297881, A348798, A348801.

A348801 a(n) = number of unsensed genus 8 maps with n edges.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 176377605783906, 43058445711817178, 5477393987229533288, 483573171728920541590, 33299663456795126129156

Offset: 0

Michael De Vlieger, Nov 01 2021

Evgeniy Krasko and Alexander Omelchenko, Enumeration of Unsensed Orientable Maps on Surfaces of a Given Genus, arXiv:1712.10139 [math.CO], 2017, see Appendix Table 4.

Column k=8 of A379439.
Cf. A238358 (rooted), A239922 (sensed).
Cf. A006387, A214814, A214815, A297880, A297881, A348798, A348800.

A380234 Triangle read by rows: T(n,k) is the number of achiral combinatorial maps with n edges and genus k, 0 <= k <= floor(n/2).

Original entry on oeis.org

1, 2, 4, 1, 14, 6, 47, 34, 4, 184, 188, 46, 761, 1040, 408, 33, 3314, 5756, 3220, 538, 14997, 32069, 23824, 6489, 398, 69886, 179408, 169336, 66150, 8506, 333884, 1009234, 1170654, 611278, 129030, 6405, 1626998, 5700548, 7930892, 5279172, 1608172, 168702, 8067786, 32341002, 52930196, 43429578, 17758601, 3080190, 128448

Offset: 0

Andrew Howroyd, Jan 17 2025

Achiral maps are also called reflexible.

			Triangle starts:
  n\k    [0]     [1]     [2]    [3]   [4]
  [0]     1;
  [1]     2;
  [2]     4,      1;
  [3]    14,      6;
  [4]    47,     34,      4;
  [5]   184,    188,     46;
  [6]   761,   1040,    408,    33;
  [7]  3314,   5756,   3220,   538;
  [8] 14997,  32069,  23824,  6489,  398;
  [9] 69886, 179408, 169336, 66150, 8506;
  ...

Andrew Howroyd, Table of n, a(n) for n = 0..120 (rows 0..20)
Evgeniy Krasko and Alexander Omelchenko, Enumeration of Unsensed Orientable Maps on Surfaces of a Given Genus, arXiv:1712.10139 [math.CO], 2017.
Evgeniy Krasko, Reflexible maps with E edges on orientable surfaces of genus G, 2017 (data file).

Row sums are A170947.
Column 0 is A006443.
Cf. A379438 (sensed), A379439 (unsensed).

cp's OEIS Frontend

A348800 a(n) = number of unsensed genus 7 maps with n edges.

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A348801 a(n) = number of unsensed genus 8 maps with n edges.

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A380234 Triangle read by rows: T(n,k) is the number of achiral combinatorial maps with n edges and genus k, 0 <= k <= floor(n/2).

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