HMMT November 2023 U16

Compute the number of tuples $\left(a_{0}, a_{1}, a_{2}, a_{3}, a_{4}, a_{5}\right)$ of (not necessarily positive) integers such that $a_{i} \leq i$ for all $0 \leq i \leq 5$ and

$$a_{0}+a_{1}+\cdots+a_{5}=6$$