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Recursive Definition (Posted on 2005-09-09) Difficulty: 4 of 5
Define H(m,n) for m≥n≥0 by

  • H(m,n)=1, if n≤1
  • H(m,n)=Σi=1..nH(m-i,minimum(i,m-i)), if n>1
  • For any integer k>0, what do you think H(k,k) represents?

    See The Solution Submitted by Bractals    
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    Some Thoughts No Subject | Comment 2 of 8 |
    k=2    H(2,2) = H(2-1,min(1,2-1)) + H(2-2,min(2,2-2)) =
    = H(1,1) + H(0,0) =
    = 1 + 1 =
    = 2

    k=3    H(3,3) = H(3-1,min(1,3-1)) + H(3-2,min(2,3-2)) +
    + H(3-3,min(3,3-3) =
    = H(2,1) + H(1,1) + H(0,0) =
    = 1 + 1 + 1 =
    = 3

    Without going further (and without proof) it seems to me that H(k,k) = k.

       

      Posted by pcbouhid on 2005-09-09 15:19:00
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