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).

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

0,2

Comments

Achiral maps are also called reflexible.

Links

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).

Example

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;
  ...

Crossrefs

Row sums are A170947.

Column 0 is A006443.

Cf. A379438 (sensed), A379439 (unsensed).

Sequence in context: A204117 A184176 A163546 * A379439 A379438 A172385

Adjacent sequences: A380231 A380232 A380233 * A380235 A380236 A380237

Keyword

nonn,tabf

Author

Andrew Howroyd, Jan 17 2025

Status

approved