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Sequence a_i shows number of times i shows up

Source: 2013 SDMO Middle School Problem 2

August 25, 2016

Problem Statement

Find all sequences (a0,a1,a2,a3)\left(a_0,a_1,a_2,a_3\right), where for each kk, 0≤k≤30\leq k\leq3, aka_k is the number of times that the number kk appears in the sequence (a0,a1,a2,a3)\left(a_0,a_1,a_2,a_3\right).
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