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?
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.
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Posted by Jer
on 2005-09-09 16:52:56 |
But can I prove it?
