The DWBC3 domino-tiling conjecture for the 20V model

Let $B_n$ be the sequence associated with 20V configurations with DWBC3 boundary conditions, and let $b_n=T({\mathcal T}_n)$ denote the number of domino tilings of the triangle ${\mathcal T}_n$. The DWBC3 conjecture. The number of configurations of the 20V model with DWBC3 boundary conditions on an $n\times n$ square grid is equal to the number of domino tilings of ${\mathcal T}_n$:

$$B_n=b_n=T({\mathcal T}_n).$$

The conjecture is motivated by agreement of the initial values of the two sequences and would identify the 20V-DWBC3 enumeration with a domino-tiling enumeration; no proof or disproof is supplied here.