Generic quadratic non-commutative algebra Hilbert-series conjecture

Let $B$ be a non-commutative algebra generated by $n$ degree-one elements with $r$ homogeneous quadratic relations; this is an algebra of type $(n,r)$. For a power series $A(z)=\sum_{i\ge0}a_i z^i$, define $[A(z)]=\sum_{i\ge0}b_i z^i$, where $b_i=a_i$ if $a_j>0$ for all $j\le i$ and $b_i=0$ otherwise. The generic quadratic Hilbert-series conjecture. If $B$ is a non-commutative generic algebra of type $(n,r)$, then

$$B(z)=\left[\frac{1}{1-nz+rz^2}\right].$$

The claim concerns the generic Hilbert series in the quadratic non-commutative case. The supplied text notes that the analogous assertion for arbitrary types is false and gives a counterexample, but provides no resolution status for this quadratic conjecture.