A380453 Number of dessins d'enfants D(n,g) with n edges of genus g, read by rows.

1, 3, 6, 1, 20, 6, 60, 33, 4, 291, 285, 48, 1310, 2115, 708, 30, 6975, 16533, 9807, 1155, 37746, 126501, 119436, 29910, 900, 215602, 972441, 1355400, 601364, 58032, 1262874, 7451679, 14561360, 10260804, 2112300, 54990, 7611156, 57167260, 150429819, 156469887, 57017238, 4764654

Offset

1,2

Comments

Note that Sum_{g>=0} D(n,g) gives A057005 which is the number of dessins d'enfants with n edges (as one would hope).

We get a new genus every two edges.

n=7 is the first time we have more dessins of genus 1 than genus 0.

Links

Table of n, a(n) for n=1..42.

Paawan Jethva, Exploring the Euler Characteristics of Dessins d’Enfants, 2023, page 15.

Ján Karabáš, Enumeration of actions of cyclic groups on orientable surfaces.

A. Mednykh and R. Nedela, Recent progress in enumeration of hypermaps, J. Math. Sci., New York 226, No. 5, 635-654 (2017) and Zap. Nauchn. Semin. POMI 446, 139-164 (2016), tables 2-8 and theorems 8-12. Theorem 12 has typos; the corrected formula can be inferred from Karabáš's tables.

Example

Triangle D(n,g) begins:
   n\g    0      1      2      3      4      ...
   1      1
   2      3
   3      6      1
   4      20     6
   5      60     33     4
   6      291    285    48
   7      1310   2115   708    30
   8      6975   16533  9807   1155
   9      37746  126501 119436 29910  900
   ...

Crossrefs

Cf. A057005.

Columns: A090371, A118094, A214819, A214820, A356694. A321710 is the rooted version.

Sequence in context: A108441 A176231 A176230 * A335227 A094445 A004158

Adjacent sequences: A380450 A380451 A380452 * A380454 A380455 A380456

Keyword

nonn,tabf

Author

Paawan Jethva, Jun 22 2025

Extensions

Rows 10-11 from Andrei Zabolotskii, Jun 28 2025

Status

approved