The extended DWBC3 conjecture for 20V configurations and domino tilings

Let $P_{n,k}$ be the pentagonal domain carrying the extended DWBC3 boundary conditions, and let ${\mathcal T}_{n,k}$ be the corresponding extended triangle whose domino tilings are counted by $T({\mathcal T}_{n,k})$. The extended DWBC3 conjecture. For all $n,k$, the number of configurations of the 20V model with extended DWBC3 boundary conditions on $P_{n,k}$ is equal to the number of domino tilings of ${\mathcal T}_{n,k}$.

The claim is based on exact agreement between the listed values of the extended 20V counts $p_{n,k}$ and the tiling counts $T({\mathcal T}_{n,k})$. The source gives no proof or disproof.