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Source: 2022 IMOC C5

September 6, 2022
combinatoricsIMOC

Problem Statement

Define a "ternary sequence" is a sequence that every number is 0,10,1 or 22. ternary sequence (x1,x2,x3,⋯ ,xn)(x_1,x_2,x_3,\cdots,x_n), define its difference to be (∣x1−x2∣,∣x2−x3∣,⋯ ,∣xn−1−xn∣)(|x_1-x_2|,|x_2-x_3|,\cdots,|x_{n-1}-x_n|) A difference will make the length of the sequence decrease by 11, so we define the "feature value" of a ternary sequence with length nn is the number left after n−1n-1 differences. How many ternary sequences has length 20232023 and feature value 00?
Proposed by CSJL
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