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%I #9 Oct 19 2017 03:14:30
%S 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,
%T 6,32,12,30,23,27,5,48,29,28,12,46,11,56,19,35,40,58,10,58,24,44,30,
%U 76,16,49,23,56,46,76,7,98,46,53,34,67,21,111,43,82,40,94,11,119,49
%N a(n) = the number of numerical semigroups with three generators and Frobenius number n.
%C A numerical semigroup is a set of natural numbers closed under addition. Its Frobenius number is the largest number not in it.
%H P. A. Garcia-Sanchez and J. C. Rosales, <a href="http://dx.doi.org/10.2140/pjm.1999.191.75">Numerical semigroups generated by intervals</a>, Pacific J. Math. 191 (1999), no. 1, 75-83.
%H J. C. Rosales and M. B. Branco, <a href="http://dx.doi.org/10.2140/pjm.2003.209.131">Irreducible numerical semigroups</a>, Pacific J. Math. 209 (2003), no. 1, 131-143.
%H J. C. Rosales, P. A. Garcia-Sanchez and J. I. Garcia-Garcia, <a href="http://dx.doi.org/10.7146/math.scand.a-14427">Every positive integer is the Frobenius number of a numerical semigroup with three generators</a>, Math. Scand. 94 (2004), no. 1, 5-12.
%e 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).
%Y Cf. A094365, A094366, A124506.
%K nonn
%O 1,5
%A Talia Harrell (zeta_lady01(AT)yahoo.com), Apr 27 2004
%E Edited by _Don Reble_, Apr 26 2007