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# Recurrence relation watch

1. The question is: Let the number of n-digit numbers such that no three consecutive numbers are the same be .

Explain why .

Struggling!
2. (Original post by Jooooshy)
The question is: Let the number of n-digit numbers such that no three consecutive numbers are the same be .

Explain why .

Struggling!
Consider the digits as a sequence.

For a sequence of n+1, we can put 9 different digits on (different in that they are not the same as the last digit in the n+1 sequence), hence the

We can only put the same digit on, if the now last two digits are different to the n'th digit, and there are of them.

Hence,,,,
3. (Original post by ghostwalker)
Consider the digits as a sequence.

For a sequence of n+1, we can put 9 different digits on (different in that they are not the same as the last digit in the n+1 sequence), hence the

We can only put the same digit on, if the now last two digits are different to the n'th digit, and there are of them.

Hence,,,,
Ah so we kind of partition on whether or not the last two digits are the same? That makes sense! I also forgot 0 could be appended to the end

Thank you!

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