As one of the IMO problems

Probability Level 3

How many numbers in binary format that have 32 bits and haven't got any block of 111 and 101 in their form?

16777216 6677056 6677057 8388608

Aaaaa Bbbbb by aaaaa bbbbb , 39, Vietnam

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1 solution

Patrick Corn
Sep 23, 2014

I got a recursion of a n = 2 ( a n − 3 + a n − 4 + a n − 5 ) + a n − 6 a_n = 2(a_{n-3} + a_{n-4} + a_{n-5}) + a_{n-6} . Not sure if there's a more direct way to do it.

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