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How many ternary (0, 1, 2) sequences of length 10 are there without any pair of consecutive digits the same?

Not sure if I understood the question correctly. It's asking for possible 10 digit number with $0, 1, 2$ and no consecutive digits.

My thoughts are if there are 10 spaces then the first space will be $3\choose 1$, second one cannot be the same with the first one so it will have to be $2\choose 1$.

So it will come down to $3\times 2^9$. Can someone correct if I'm wrong ?

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    $\begingroup$ There is no correction necessary - you have done this correctly $\endgroup$ – Keeran Brabazon Oct 19 '13 at 19:11
  • $\begingroup$ Looks good to me. $\endgroup$ – Kieran Cooney Oct 19 '13 at 19:11
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    $\begingroup$ I would simply add one thing: "$\ldots$ second one cannot be the same with the first one so it will have to be $2 \choose 1$, and the same holds for the remaining eight." $\endgroup$ – Théophile Jan 18 '15 at 0:05
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This is correct...................

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    $\begingroup$ LOL at your clever use of periods................................................................................ $\endgroup$ – heropup Dec 17 '14 at 19:25
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    $\begingroup$ @heropup: it had been edited incorrectly and I wrote an answer pointing out the problem. Then I noticed that there was an edit and that OP had it right, but there was no answer. I needed some more characters to meet the minimum of 30 $\endgroup$ – Ross Millikan Dec 17 '14 at 19:27

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