Terao's conjecture does not extend to weak combinatorics

In this work we study line arrangements consisting in lines passing through three non aligned points. We call them triangular arrangements. We prove that any of this arrangement is associated to another one with the same combinatorics, construted by removing lines to a Ceva arrangement. We then describe a combinatorics for any possible splitting type of free logarithmic bundles associated to a triangular arrangement. Finally, we give two triangular arrangements having the same weak combinatorics (that means the same number t i of points with multiplicity i, i $\ge$ 2), such that one is free but the other one is not.