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An ascent sequence of length $n$ is a nonnegative integer sequence $x=x_{1}x_{2}... x_{n}$ such that $x_{1}=0$ and $x_{i}\\leq \\asc(x_{1}x_{2}...x_{i-1})+1$ for all $1<i\\leq n$, where $\\asc(x_{1}x_{2}...x_{i-1})$ is the number of ascents in the sequence $x_{1}x_{2}... x_{i-1}$. We let $\\cA_n$ stand for the set of such sequences and use $\\cA_n(p)$ for the subset of sequences avoiding a pattern $p$. 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