Initially, there are 3^ 80 particles at the origin (0,0) . At each...

Initially, there are $3^{80}$ particles at the origin $(0,0)$. At each step the particles are moved to points above the $x$-axis as follows: if there are $n$ particles at any point ( $x, y$ ), then \left[\frac{n}{3}\right]$of them are moved to$(x+1, y+1),\left[\frac{n}{3}\right]$are moved to$(x, y+1)$and the remaining to$(x-1, y+1)$. For example, after the first step, there are$3{ }^{79}$particles each at$(1,1),(0,1)$and$(-1,1)$. After the second step, there are$3^{78}$particles each at$(-2,2)$and$(2,2), 2 \times 3^{78}$particles each at$(-1,2)$and$(1,2)$, and$3^{79}$particle at$(0,2)$. After 80 steps, the number of particles at$(79,80) is: