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Number of words with n digits (IMO SL 1987-P14)

Source:

August 19, 2010
symmetrycombinatoricsCombinatorics of wordscountingDigitsrecurrence relationIMO Shortlist

Problem Statement

How many words with nn digits can be formed from the alphabet {0,1,2,3,4}\{0, 1, 2, 3, 4\}, if neighboring digits must differ by exactly one?
Proposed by Germany, FR.
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