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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 But can I prove it? | Comment 5 of 7 |

    I only went up to 9 and then looked up my answer on the OEIS...

    the likely result is the partition numbers.

    p(k) is the number of ways k can be written as the sum of 1 or more positive integers.

    For example p(4) = 5 because

    4 = 3+1 = 2+2 = 2+1+1 = 1+1+1+1 [5 ways]

    It makes sense that the sequence of partion numbers is sort of recursive, but it may be hard to show that this particular recursive sequence does generate the partition numbers.

     


      Posted by Jer on 2005-09-09 16:52:56
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