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A team is to play $n$ games in a row. In how many ways could they play this series of games without losing two games in a row.

There are $2^n$ total games to be played. The number of games without consecutive losses would be $2^N$ - (Number of games with at least one consecutive loss).

I'm having a hard time counting the number of games with at least one consecutive loss. In particular, I can't think of a way to count the number of games with $m$ consecutive losses.

Could someone provide some guidance?

Demetri Pananos
  • 3,192
  • We have this question many times on the site. It is usually posed as a bit string without two $1$s (alternately two $0$s) in a row. You can search for Fibonacci. I cited two and the one cited in the closure cites many more. – Ross Millikan Jul 20 '17 at 04:37
  • @RossMillikan Dope, thanks – Demetri Pananos Jul 20 '17 at 04:40

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