A094367 a(n) = the number of numerical semigroups with three generators and Frobenius number n.

1, 1, 1, 1, 3, 1, 5, 2, 4, 4, 7, 1, 11, 7, 5, 7, 14, 5, 17, 6, 9, 16, 21, 2, 19, 15, 19, 10, 28, 6, 32, 12, 30, 23, 27, 5, 48, 29, 28, 12, 46, 11, 56, 19, 35, 40, 58, 10, 58, 24, 44, 30, 76, 16, 49, 23, 56, 46, 76, 7, 98, 46, 53, 34, 67, 21, 111, 43, 82, 40, 94, 11, 119, 49

Offset: 1

Author

Talia Harrell (zeta_lady01(AT)yahoo.com), Apr 27 2004

Keywords

• nonn

Comments

A numerical semigroup is a set of natural numbers closed under addition. Its Frobenius number is the largest number not in it.

Examples

			a(10)=4 because there are four such semigroups with Frobenius number 10. Their complements (and a generating triple) are: {1,2,3,5,6,10} (4,7,9); {1,2,3,5,6,9,10} (4,7,13); {1,2,4,5,7,10} (3,8,13); {1,2,4,5,7,8,10} (3,11,13).
		

Links

• P. A. Garcia-Sanchez and J. C. Rosales, Numerical semigroups generated by intervals, Pacific J. Math. 191 (1999), no. 1, 75-83.
• J. C. Rosales and M. B. Branco, Irreducible numerical semigroups, Pacific J. Math. 209 (2003), no. 1, 131-143.
• J. C. Rosales, P. A. Garcia-Sanchez and J. I. Garcia-Garcia, Every positive integer is the Frobenius number of a numerical semigroup with three generators, Math. Scand. 94 (2004), no. 1, 5-12.

Crossrefs

Cf. A094365, A094366, A124506.

Extensions

Edited by Don Reble, Apr 26 2007