[seqfan] Computing the number of numerical semigroups using generating functions

[Jonathan Post]

This table (p.5) deserves a place in the OEIS wiki.

Table 1. Number of numerical semigroups with given genus g and multiplicity m.

http://arxiv.org/abs/0901.1228

Computing the number of numerical semigroups using generating functions
Authors: Victor Blanco, Pedro A. Garcia-Sanchez, Justo Puerto
(Submitted on 9 Jan 2009 (v1), last revised 23 Dec 2009 (this version, v3))

    Abstract: This paper presents a new methodology to count the
number of numerical semigroups of given genus or Frobenius number. We
apply generating function tools to the bounded polyhedron that
classifies the semigroups with given genus (or Frobenius number) and
multiplicity. First, we give theoretical results about the
polynomial-time complexity of counting the number of these semigroups.
We also illustrate the methodology analyzing the cases of multiplicity
3 and 4 where some formulas for the number of numerical semigroups for
any genus and Frobenius number are obtained.