We give a simple explanation of numerical experiments of V. Arnold with two sequences of symmetric numerical semigroups, S(4,6+4k,87−4k) and S(9,3+9k,85−9k) generated by three elements. We present a generalization of these sequences by numerical semigroups $\mathsf{S}(r_{1}^{2},r_{1}r_{2}+r_{1}^{2}k,r_{3}-r_{1}^{2}k)$ , k∈ℤ, r 1,r 2,r 3∈ℤ+, r 1≥2 and gcd(r 1,r 2)=gcd(r 1,r 3)=1, and calculate their universal Frobenius number Φ(r 1,r 2,r 3) for the wide range of k providing semigroups be symmetric. We show that this type of semigroups admit also nonsymmetric representatives. We describe the reduction of the minimal generating sets of these semigroups up to $\{r_{1}^{2},r_{3}-r_{1}^{2}k\}$ for sporadic values of k and find these values by solving the quadratic Diophantine equation.