Question 143
How many 9-term sequences $a_{1}, \ldots, a_{9}$ of nonnegative integers are there such that
- $0 \leq a_{i} \lt i$ for all $i = 1, \ldots, 9$; and
- there are no ordered triples $(i, j, k)$ with $1 \leq i \lt j \lt k \leq 9$, such that $a_{i}, a_{j}, a_{k}$ are all distinct?
- $0 \leq a_{i} \lt i$ for all $i = 1, \ldots, 9$; and
- there are no ordered triples $(i, j, k)$ with $1 \leq i \lt j \lt k \leq 9$, such that $a_{i}, a_{j}, a_{k}$ are all distinct?