Impossible Dot-Product Sums

On the side $BC$ of an equilateral triangle $ABC$ of side length $1$, take $n$ equally spaced interior points ($n\geqslant 2$), labeled $P_1,P_2,\dots,P_{n-1}$ in the direction of $\overrightarrow{BC}$. Let

Among the four numbers $\dfrac{29}4$, $\dfrac{91}{10}$, $\dfrac{197}{18}$, $\dfrac{232}{33}$, determine how many cannot be a value of $T_n$.