  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 S(r_1^2,r_1r_2+r_1^2k,r_3-r_1^2k),
k\in{\mathbb Z}, r_1,r_2,r_3\in{\mathbb Z}^+, r_1\geq 2 and
\gcd(r_1,r_2)=\gcd(r_1,r_3)=1, and calculate their universal Frobenius number
Phi(r_1,r_2,r_3) for the wide range of k providing semigroups be symmetric. We
show that this kind 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_1^2k} for sporadic values of k and find these values by solving
the quadratic Diophantine equation.
