Counterexample to a conjecture about dihedral quandle

It was conjectured that the augmentation ideal of a dihedral quandle of even order $n>2$ satisfies $\mathrm{\mid }{\mathrm{\Delta }}^k({\text{R}}_n)\mathrm{/}{\mathrm{\Delta }}^{k+1}({\text{R}}_n)\mathrm{\mid }=n$ for all $k\ge 2$. In this article we provide a counterexample against this conjecture.