[離散] 遞迴

[suruys (也只是 蜉蝣)]

不好意思，想不到這題怎麼處理，希望有人可以給點想法或見解。

題目：

  Find a system of recurrence relations for the number of n-digit binary

  sequences with k adjacent pairs of 1s and no adjacent pairs of 0s.


  PS：是指k組相鄰的1和沒有相鄰的0嗎？


答案：

  a_n,k = a_n,k,0 +a_n,k,1

  a_n,k,0 = a_(n-1),k,1

  a_n,k,1 = a_(n-1),k,0 + a_(n-1),(k-1),1

  where a_n,k,0 = such sequences staring with a 1

        a_n,k,1 = such sequences staring with a 0



謝謝！



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