The Fibonacci numbers $F_n$ can be given by
$$\sum_{k\geq0}F_kx^k=\frac{x}{1-x-x^2}.$$
Among many many properties of this sequence, consider the following two results:

(1) the [coefficients of the infinite product][1] $\prod_{i=2}^{\infty}(1-x^{F_i})$ are $-1, 0$ or $+1$;

(2) the [coefficients of the finite product][2] $\prod_{i=2}^N(1-x^{F_i})$ are $-1, 0$ or $+1$.

It is almost irresistible to look for more. To this end, consider for example, the tribonacci sequences given by
$$\sum_{k\geq0}T_kx^k=\frac{x^2}{1-x-x^2-x^3}.$$

>**QUESTION.** Are the coefficients of the finite or infinite products 
$$\prod_{i=3}^N(1-x^{T_i}) \qquad \text{and} \qquad
\prod_{i=3}^{\infty}(1-x^{T_i})$$
bounded? What is the best bound?

**Remark.** An affirmative answer lends itself further generalization of this assessment.

[1]: https://arxiv.org/abs/math/0409418
[2]: https://www.fq.math.ca/Papers1/46_47-1/Zhao_12-08.pdf