Super-Collider

At time \(t = 0\) a particle is at point \(0\) on the real line. At time \(t=1\), the particle divides into two and instantaneously after division, one particle moves one unit to the left and the other moves one unit to the right. At time \(t = 2\), each of these particles gets divided into \(2\) and one of the two new particles move to the right by 1 unit and the other moves to the left by 1 unit. Whenever two particles meet on the real line they annihilate (destroy) each other completely leaving not a single trace behind.

How many particles will be there at time \(t = 8193\)?

Image credit: Wikipedia CERN
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