Numerical Terao's conjecture for plane curves with ordinary quasi-homogeneous singularities

Let $C_{1}, C_{2}$ be reduced curves in $\mathbb{P}^{2}_{\mathbb{C}}$ whose irreducible components are smooth and whose singularities are ordinary quasi-homogeneous singularities. For a curve $C$, let $W(C)$ denote its weak combinatorics, recording the numbers of irreducible components of each degree and the numbers of multiple intersections of each multiplicity. Numerical Terao's conjecture. If

$$W(C_{1})=W(C_{2})$$

and $C_{1}$ is free, then $C_{2}$ is free. The conjecture asserts that freeness is determined by the weak combinatorics. It is false, specifically for triangular line arrangements, so the statement is refuted.