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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

%I

%S 1,1,2,2,5,4,11,10,21,22,51,40,106,103,200,205,465,405,961,900,1828,

%T 1913,4096,3578,8273,8175,16132,16267,34903,31822,70854,68681,137391,

%U 140661,292081,270258,591443,582453,1156012

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

%H S. R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/">Monoids of natural numbers</a>

%H S. R. Finch, <a href="/A066062/a066062.pdf">Monoids of natural numbers</a>, March 17, 2009. [Cached copy, with permission of the author]

%H J. C. Rosales, P. A. Garcia-Sanchez, J. I. Garcia-Garcia and J. A. Jimenez-Madrid, <a href="https://doi.org/10.1016/j.jpaa.2003.10.024">Fundamental gaps in numerical semigroups</a>, Journal of Pure and Applied Algebra 189 (2004) 301-313.

%H Clayton Cristiano Silva, <a href="http://www.ime.unicamp.br/~ftorres/ENSINO/MONOGRAFIAS/Clayton.pdf">Irreducible Numerical Semigroups</a>, University of Campinas, São Paulo, Brazil (2019).

%e 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>...

%o (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.

%Y Cf. A158206. [From _Steven Finch_, Mar 13 2009]

%K nonn

%O 1,3

%A P. A. Garcia-Sanchez (pedro(AT)ugr.es), Dec 18 2006

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Last modified November 14 15:15 EST 2019. Contains 329126 sequences. (Running on oeis4.)