GAIC Math 2024 Problem 139

Let sequence $a_{1}, a_{2}, \cdots, a_{10}$ satisfy $1 \leqslant a_{1} \leqslant{l} a_{2} \leqslant \cdots \leqslant a_{10} \leqslant 40$, $a_{4} \geqslant6$, and $\log _{2}\left(\left|a_{i}-i\right|+1\right) \in \mathbf{N}(i=1,2, \cdots, 10)$ The number of such sequences is _____.