

A124506


Number of numerical semigroups with Frobenius number n; that is, numerical semigroups for which the largest integer not belonging to them is n.


5



1, 1, 2, 2, 5, 4, 11, 10, 21, 22, 51, 40, 106, 103, 200, 205, 465, 405, 961, 900, 1828, 1913, 4096, 3578, 8273, 8175, 16132, 16267, 34903, 31822, 70854, 68681, 137391, 140661, 292081, 270258, 591443, 582453, 1156012
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OFFSET

1,3


LINKS

Table of n, a(n) for n=1..39.
S. R. Finch, Monoids of natural numbers
S. R. Finch, Monoids of natural numbers, March 17, 2009. [Cached copy, with permission of the author]
J. C. Rosales, P. A. GarciaSanchez, J. I. GarciaGarcia and J. A. JimenezMadrid, Fundamental gaps in numerical semigroups, Journal of Pure and Applied Algebra 189 (2004) 301313.
Clayton Cristiano Silva, Irreducible Numerical Semigroups, University of Campinas, São Paulo, Brazil (2019).


EXAMPLE

The first term is 1 because <2,3>={0,2,3,4,...} is the only numerical semigroup with Frobenius number 1. The second is also 1 because <3,4,5> is the only numerical semigroup with Frobenius number 2. For n=3, one gets <2,5> and <4,5,6,7>...


PROG

(GAP) The sequence was originally generated by a C program and a Haskell script. The sequence can be obtained by using the function NumericalSemigroupsWithFrobeniusNumber included in the numericalsgps GAP package.


CROSSREFS

Cf. A158206. [From Steven Finch, Mar 13 2009]
Sequence in context: A292263 A338528 A238624 * A264687 A112471 A144366
Adjacent sequences: A124503 A124504 A124505 * A124507 A124508 A124509


KEYWORD

nonn


AUTHOR

P. A. GarciaSanchez (pedro(AT)ugr.es), Dec 18 2006


STATUS

approved



