Let $n$ be a posititve integer and let $M$ the set of all all integer cordinates $(a,b,c)$ such that $0 \le a,b,c \le n$. A frog needs to go from the point $(0,0,0)$ to the point $(n,n,n)$ with the following rules: $\cdot$ The frog can jump only in points of $M$ $\cdot$ The frog can't jump more than $1$ time over the same point. $\cdot$ In each jump the frog can go from $(x,y,z)$ to $(x+1,y,z)$, $(x,y+1,z)$, $(x,y,z+1)$ or $(x,y,z-1)$ In how many ways the Frog can make his target?
Problem
Source: Bolivian Cono Sur TST 2021 Day 2 P2
Tags: combinatorics, paths, Bolivia, Cono Sur TST, TST