We investigate the integer sequence $\left(t_{n}\right)_{n\in\mathbb{Z}}$ defined by $t_{n}=0$ if $n\leq0$, $t_{1}=1$, and $t_{n}=\sum_{i=1}^{n-1}t_{n-t_{i}}$ for $n \geq 2$. This sequence has the following properties: if we consider $f_{n}(X):=-1+\sum_{i=1}^{n}X^{t_{i}}$ and take $x_{n}$ to be the real positive number such that $f_{n}(x_{n})=0$, then

$$\lim_{n\rightarrow\infty}\frac{t_{n}}{t_{n+1}}=\lim_{n\rightarrow\infty}x_{n}=0.410098516\cdots$$

Moreover, if $u$ is the real positive number such that $1=\sum_{i=1}^{\infty} u^{-t_i}$, then there is a positive constant $M$ such that $t_n\sim Mu^n$.