Counting numerical semigroups by genus and some cases of a question of Wilf

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Fibonacci-like growth of numerical semigroups of a given genus (2011, background): “, little has been established concerning the relationship between ng and ng+1. In particular, it remains open whether ng+2 ≥ ng+1 +ng, as conjectured in [2] and the conjecture that ng+1 ≥ ng given in [6] remains unveriﬁed for a ﬁnite but large number of g. In addition, we have conﬁrmed Zhao’s conjec”
Wilf’s conjecture and Macaulay’s theorem (2017, methodology): “6 The case q = 2 It was shown in [11] that Wilf’s conjecture holds for q = 2, i.”