|
%I #8 Oct 19 2017 03:14:30
%S 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,
%T 29,12,29,23,24,5,46,29,26,12,42,11,53,19,34,40,53,10,55,24,42,30,72,
%U 16,46,23,55,46,70,7,96,46,51,34,63,21,108,43,80,40,88,11,117,49,60
%N Number of numerical semigroups with three nonextraneous 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.
%C A generator is extraneous if it can be generated by other generators.
%H J. L. Davison, <a href="https://doi.org/10.1006/jnth.1994.1071">On the linear Diophantine problem of Frobenius numbers</a>, J. Number Theory 48 (1994), p353-363.
%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.
%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.
%e 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).
%Y Cf. A094366 (2 generators), A094367 (3 generators).
%K nonn
%O 1,7
%A Kaye A. Archer (godchaser_2(AT)hotmail.com), May 06 2004
%E Edited by _Don Reble_, Apr 26 2007
|
