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IMC 2018 P8

Source: IMC 2018 P8

July 25, 2018
college contestsimc2018combinatorics

Problem Statement

Let Ω={(x,y,z)∈Z3:y+1⩾x⩾y⩾z⩾0}\Omega =\{ (x,y,z)\in \mathbb{Z}^3:y+1\geqslant x\geqslant y\geqslant z\geqslant 0\}. A frog moves along the points of Ω\Omega by jumps of length 11. For every positive integer nn, determine the number of paths the frog can take to reach (n,n,n)(n,n,n) starting from (0,0,0)(0,0,0) in exactly 3n3n jumps.
Proposed by Fedor Petrov and Anatoly Vershik, St. Petersburg State University
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