Siddharth's Paths

A grasshopper starts on the origin of the complex plane. Each second, if the grasshopper is at the point \((m,n)\) it jumps to \((m+6,n+9)\) or \((m+9,n+6)\). How many different paths are there for the grasshopper to land on the line \( x= 36 \)?

This problem is posed by Siddharth P..

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