OEIS conjecture for the distribution of mesh pattern 3

For each permutation length, let the distribution of a mesh pattern be the sequence counting permutations according to their number of occurrences of that pattern. Let $\operatorname{DELTA}$ denote the continued-fraction operator determined by

$$[r_0,r_1,\ldots]\operatorname{DELTA}[s_0,s_1,\ldots]$$

with generating function

$$\frac{1}{1-\frac{r_0x+s_0xy}{1-\frac{r_1x+s_1xy}{1-\frac{r_2x+s_2xy}{1-\ldots}}}}.$$

The conjecture concerns mesh pattern Nr. 3, whose shaded cells and marked points are specified by the source diagram.

Distribution conjecture for mesh pattern 3. The distribution of mesh pattern Nr. 3 is the triangle, read by rows, given by

$$(1,0,2,1,3,2,4,3,5,4,6,5,7,6,\ldots)\ \operatorname{DELTA}\ (0,1,0,1,0,1,0,1,0,1,\ldots).$$

The claim is explicitly attributed to OEIS sequence A200545, with the operator defined through OEIS sequence A084938; no proof or resolution is supplied in the paper, so its status remains open.