A094365 Number of numerical semigroups with three nonextraneous generators and Frobenius number n.

0, 1, 0, 1, 1, 1, 3, 2, 3, 4, 4, 1, 9, 7, 4, 7, 11, 5, 14, 6, 8, 16, 17, 2, 17, 15, 17, 10, 24, 6, 29, 12, 29, 23, 24, 5, 46, 29, 26, 12, 42, 11, 53, 19, 34, 40, 53, 10, 55, 24, 42, 30, 72, 16, 46, 23, 55, 46, 70, 7, 96, 46, 51, 34, 63, 21, 108, 43, 80, 40, 88, 11, 117, 49, 60

Offset: 1

Author

Kaye A. Archer (godchaser_2(AT)hotmail.com), May 06 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.

A generator is extraneous if it can be generated by other generators.

Examples

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

Links

• J. L. Davison, On the linear Diophantine problem of Frobenius numbers, J. Number Theory 48 (1994), p353-363.
• 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.
• J. C. Rosales and M. B. Branco, Irreducible numerical semigroups, Pacific J. Math. 209 (2003), no. 1, 131-143.

Crossrefs

Cf. A094366 (2 generators), A094367 (3 generators).

Extensions

Edited by Don Reble, Apr 26 2007