A158278 Number of symmetric numerical semigroups with Frobenius number 2*n-1; that is, symmetric numerical semigroups for which the largest integer not belonging to them is 2*n-1.
1, 1, 2, 3, 3, 6, 8, 7, 15, 20, 18, 36, 44, 45, 83, 109, 101, 174, 246, 227
Offset: 1
Examples
a(3)=2: the only 2 symmetric semigroups with Frobenius number 5=2*3-1 are generated by {3, 4} and {2, 7}.
Links
- CombOS - Combinatorial Object Server, Generate numerical semigroups
- 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).
Formula
a(n) = A158206(2*n-1).