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Recurrence relations

  1. Apr 24, 2009 #1
    Hello:

    I am asked to find a recurrence relation for the number of n letter sequences composed of A, B, C where every A that is not in the last position is followed by a B.

    So, would this be:

    A| (we have A(n-2) sequences) + 0 if A is in the last position
    B| we have A(n-1)
    C| we have A(n-1)

    So does this mean that A(n) = A(n-1) + 2*A(n-1)? But this seems simplistic ....

    Thanks.
     
  2. jcsd
  3. Apr 24, 2009 #2

    lanedance

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    Homework Helper

    hi bodensee9

    I'm not too sure what you mean by A(n), if we let N(n) be number of terms given n letters, i would start by looking at n=1, and would take it to mean you can have:
    A or
    B or
    C
    so N(1) = 3, with 1 term ending in A

    then for n=2
    AB only (1)
    BA, BB, BC (3)
    CA, CB, CC (3)
    so N(2) = 7, with 2 terms ending in A...
     
  4. Apr 24, 2009 #3
    Hello:

    Thanks, I solved it I think.

    A(n-1) means "a sub n-1" because I don't know how to type subscript on here.

    I took your approach, and broke things down into
    A
    B
    C, etc.
     
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