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A094367
a(n) = the number of numerical semigroups with three generators and Frobenius number n.
2
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
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
KEYWORD
nonn
AUTHOR
Talia Harrell (zeta_lady01(AT)yahoo.com), Apr 27 2004
EXTENSIONS
Edited by Don Reble, Apr 26 2007
STATUS
approved