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6

Part of 2016 South East Mathematical Olympiad

Problems(1)

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Source: China South East Mathematical Olympiad 2016 Grade 10 Prob. 6

7/31/2016
Toss the coin nn times, assume that each time, only appear only head or tail Let a(n)a(n) denote number of way that head appear in multiple of 33 times among nn times Let b(n)b(n) denote numbe of way that head appear in multiple of 66 times among nn times (1)(1) Find a(2016)a(2016) and b(2016)b(2016) (2)(2) Find the number of positive integer n≤2016n\leq 2016 that 2b(n)−a(n)≥02b(n)-a(n)\geq 0
combinatorics