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a_i elements of sequence equal to i

Source: Portugal OPM 2015 p5

May 15, 2024
number theorycombinatorics

Problem Statement

A sequence of integers (a0,...,ak)(a_0,...,a_k) is said to be medaled if, for each i=0,...,ki = 0,...,k, there are exactly aia_i elements of the sequence equal to ii. For example, (1,2,1,0)(1,2,1,0) is a medaled seqence. Indicates all medaled sequences (a0,...,a2015)(a_0,...,a_{2015}).
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