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

1,5

Comments

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

Links

Table of n, a(n) for n=1..74.

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.

Example

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).

Crossrefs

Cf. A094365, A094366, A124506.

Sequence in context: A185051 A095026 A184997 * A092368 A225080 A276505

Adjacent sequences: A094364 A094365 A094366 * A094368 A094369 A094370

Keyword

nonn

Author

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

Extensions

Edited by Don Reble, Apr 26 2007

Status

approved