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The maximum number of nodes expanded during a breadth-first search can be calculated using the following formula.

N = 1 + b + b² + ......+ b^d.

Given b=3         (b is branching factor)

d = 4.            (d is depth)

N = 1+ 3 + 3^2 + 3^3 + 3^4 = 121.
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