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IOQM 2022-23 P-22

Source:

October 30, 2022
combinatoricsIOQM

Problem Statement

A binary sequence is a sequence in which each term is equal to 00 or 11. A binary sequence is called friendly\text{friendly} if each term is adjacent to at least on term that is equal to 11. For example , the sequence 0,1,1,0,0,1,1,10,1,1,0,0,1,1,1 is friendly\text{friendly}. Let FnF_{n} denote the number of friendly\text{friendly} binary sequences with nn terms. Find the smallest positive integer n≥2n\ge 2 such that Fn>100F_{n}>100
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