Tribonacci to Infinity

Let TT be the nonnegative integer sequence defined by T0=0T1=1T2=1Tn=Tn1+Tn2+ Tn3  (for n3).\begin{aligned} T_0 &= 0 \\ T_1 &= 1 \\ T_2 &= 1 \\ T_n &= T_{n-1} + T_{n-2} +\ T_{n-3}\ \ (\text{for }n \geq 3). \end{aligned} Also let Q=limnTnTn1.Q = \lim_{n\to\infty}\frac{T_n}{T_{n-1}}. Find the value of Q3Q2Q.Q^3 - Q^2 - Q.

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