
COMMENTS

The theory of dessins d'enfants was initiated by A. Grothendieck. "In this work, using the matrix model approach... we listed all the dessins d'enfants with no more than 4 edges. There are two 1edge dessins, both of them are of genus zero, fifteen 2edge dessins, among them only one is of genus 1, twenty 3edge dessins: 14 sperical [sic] and 6 of genus 1 and one hundred seven 4edge dessins: 57 spherical dessins, 46 dessins of genus 1 and 4 dessins of genus 2. The total number of dessins is 134."
Note: The fifteen for n=2 is a typo, it should be 5. The sum: 2+5+20+107=134 adds up if we replace fifteen by 5, and moreover, the section on 2edge dessins lists all 5 (not fifteen) dessins. The correct version of this sequence is given by A170946.  Mark van Hoeij, Jan 23 2011


LINKS

Table of n, a(n) for n=1..4.
N. M. Adrianov, N. Ya. Amburg, V. A. Dremov, Yu. A. Levitskaya, E. M. Kreines, Yu. Yu. Kochetkov, V. F. Nasretdinova and G. B. Shabat, Catalog of dessins d'enfants with <= 4 edges, arXiv:0710.2658 [math.AG], 2007.
