A sequence related to the shape $2^{x}+2^{y}+2^{z}$

Notation: here $\left(\begin{array}{c} n \\ k \\ \end {array}\right)$ $(n\geq k\geq 0)$ is the binomial coefficient.

Let $f(x,y,z)=2^{x}+2^{y}+2^{z}$ .Note that $f(21,22,23)$ is the $\left(\begin{array}{c} 24 \\ 3 \\ \end {array}\right) =2024_{th}$ item of seqence $\{a_{n}\}$ ,i.e. $a_{2024}$ . Thus $a_{2018}=f(15,22,23)$ ,the answer is $15+22+23=\boxed{60}$ .