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For any numerical semigroup S, there are infinitely many numerical symmetric semigroups T such that S = T/2 (see below for the definition of T/2) is their half. We are studying the Betti numbers of the numerical semigroup ring K[T ] when S is a 3-generated numerical semigroup or telescopic. We also consider 4-generated symmetric semigroups and the so called 4-irreducible numerical semigroups.<br /><br />