Fibonacci-like growth of numerical semigroups of a given genus

We give an asymptotic estimate of the number of numerical semigroups of a given genus. In particular, if n(g) is the number of numerical semigroups of genus g, we prove that lim(g ->infinity) n(g)phi(-g) = S where phi = 1+root 5/2 is the golden ratio and S is a constant, resolving several related conjectures concerning the growth of n(g) . In addition, we show that the proportion of numerical semigroups of genus g satisfying f < 3m approaches 1 as g ->infinity, where m is the multiplicity and f is the Frobenius number.