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

1,7

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.

Links

Table of n, a(n) for n=1..75.

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.

Example

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).

Crossrefs

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

Sequence in context: A221529 A105161 A275769 * A272886 A098822 A131597

Adjacent sequences: A094362 A094363 A094364 * A094366 A094367 A094368

Keyword

nonn

Author

Kaye A. Archer (godchaser_2(AT)hotmail.com), May 06 2004

Extensions

Edited by Don Reble, Apr 26 2007

Status

approved