Tribonacci to Infinity
Number Theory
Level
3
Let \(T\) be the nonnegative integer sequence defined by \[T_0 = 0 \\ T_1 = 1 \\ T_2 = 1 \\ T_n = T_{n-1} + T_{n-2} +\ T_{n-3},\ n \geq 3\] Also let \[Q = \lim_{n\to\infty}\frac{T_n}{T_{n-1}}\] Find the value of \[Q^3 - Q^2 - Q\]
by
Caleb Townsend