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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
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 (list; graph; refs; listen; history; text; internal format)
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. Garcia-Sanchez, J. I. Garcia-Garcia and J. A. Jimenez-Madrid, Fundamental gaps in numerical semigroups, Journal of Pure and Applied Algebra 189 (2004) 301-313.

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

STATUS

approved

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Last modified December 6 10:23 EST 2022. Contains 358630 sequences. (Running on oeis4.)